NillaHedge
User Guide
Version 1.0
NillaHedge is a set of tools built
on a common database that allows you to manage your stock and option holdings,
analyze option issues, explore hedging strategies, and compare how interest
rate changes affect option issues and your portfolio of option positions. Following is a brief introduction to the
capabilities of this Pocket-PC application software, starting with an overview
of the main menus.
NillaHedge is not a
document-centric application, which means upon invocation all you’ll see is the
main menu and a blank screen. Switcher
and similar utilities typically only include applications with open document
windows in their list of running applications - the blank window gives Switcher
something to find. If you don’t have
Switcher or it’s equivalent, a tray icon will be available whenever NillaHedge is not the front most application.
When you first open NillaHedge,
you’ll see the menu at right.
NillaHedge uses a database to
store instrument definitions and portfolio positions that you create while
using it. All instrument definitions and
portfolio positions created are immediately committed to the database, so there’s
no need to save at the end of a session.
Just quit.
Open Database
Given the personal nature of Pocket-PCs, NillaHedge
assumes that there is only one user and one database - it opens a database in a
default directory upon invocation so you can get right to work. The only time
you’ll need to use Open Database is after you have previously closed the
database. This menu item is only enabled
when the database is currently closed.
Close Database
If you can’t choose database directories, you might ask why
include Open Database and Close Database at all? The answer is that ActiveSync won’t sync open
files and an open database will probably have several files open. Therefore, if you ever want your database
backed up, you can use Close Database to close it manually and then reopen it
after ActiveSync has finished. This menu
item is only enabled when the database is currently open.
The Edit menu is the entry point for creating and
subsequently modifying instrument definitions and positions based on those
definitions. Supported instruments
include stocks and vanilla stock options (i.e. puts and calls). It also provides the entry point to the NillaHedge’s two preferences dialogs. All Edit menu items are always enabled.
The Stock Definition Dialog is a structured view of the data
that defines a stock to the tools in NillaHedge,
including its market price, volatility, and dividends.
The Option Definition Dialog is a structured view of the
data that defines a vanilla stock option to the tools in NillaHedge,
including its market price, strike price, expiration date, underlying stock
symbol, and whether it’s a put or a call option.
The Positions dialog is your entry point for creating a
position in a option or stock issue. It captures the purchase date, number of
units in the position, and the cost of the position. It also captures a ‘Note’ field, allowing you
to annotate a transaction number or a source of cash for the transaction, etc.
It also displays any positions previously created for the
specified option or stock issue, including purchase date, number of shares or
options, the original cost of the position, its current market value, the
capital gain (loss), any dividend income that would have been generated since the
purchase date, the net gain (capital gain plus income), the annualized yield
that the net gain represents, and any note you may have entered when you
created the position. If the underlying
issue is an option, the income column is replaced by the exercise value of the
options in the position.
If you read the previous section on the Positions dialog,
you can see that there are quite a few columns of data computed for each
position. To manage that complexity
within the confines of a small screen, each of the columns in the Positions
dialog’s list of defined positions can be made invisible by un-checking the
associated check box in the Position List Options dialog. The left column of preferences affects the
display of columns in the Positions dialog while the right column of
preferences affects the display of columns in the Portfolio Navigator.
The Confirmation Options Dialog controls behaviors spanning
various dialogs. Two preferences affect
behavior within definition dialogs (where you define a stock or an option
issue), two affect behavior within the Option Analyzer dialog, two affect
behaviors within the Positions dialog, and one affect behaviors within the
Option Chain Retriever.
The Tools menu assembles a variety of tools in one place to
accomplish a variety of tasks. One pulls
option prices and other relevant information from the Internet, one is
analytical, four are graphical, and two report the current state of your
portfolio – one hierarchically, the other as a plain text transcript. Following is a brief introduction to each.
If you can access the internet from your Pocket-PC, the
Option Chain Retriever will retrieve current prices, trading volume, and
related information for options derived from a given exchange registered stock
symbol. The Option Chain Retriever
allows you to check current market prices, update the market price of existing
option definitions, save new option definitions to the database, and update the
market price of the stock underlying the option chain. This menu item is always enabled.
Option Analyzer
The Option Analyzer’s primary purpose is to report Black-Scholes value, a half dozen Greeks, elasticity, implied
volatility, and the probability of closing in the money. Of secondary importance is the ability to
experiment with alternative values of the risk free rate and the underlying
stock’s volatility and market price to observe how such changes will affect the
option’s market value. This menu item
will be disabled if there are no options defined in the database.
The Hedge Explorer
is a graphical tool displaying profit/loss curves for multi-issue positions
consisting of up to three options on the same underlying stock, possibly including
the stock itself. The Hedge Explorer
supports ratio spreads and short positions and allows the user to modify the
evaluation date, risk free rate, stock price and volatility. It displays the profit/loss curve for the
constituent issues as well as the aggregate profitability. This menu item is disabled when there are no
stocks or options defined in the database.
Rate Sensitivity Explorer
The Rate
Sensitivity Explorer provides a graphical view of how the value of options and
portfolios of options are affected by interest rate changes. This menu item is disabled when there are no
options defined in the database.
Time Decay Explorer
The Time Decay
Explorer is a graphical tool which plots option values versus time. It supports two modes of operation – one
completely based on Black-Scholes value, the other
incorporating the option’s current market price. This menu item is disabled when there are no
options defined in the database.
Volatility-Value Explorer
The
Volatility-Value Explorer is a graphical tool which plots relative option value
versus relative volatility of the underlying stock. Relative values are simply ratios of
prospective volatility or option value divided by the currently stored value
for the stock’s volatility or the option’s current Black-Scholes
value, respectively. This menu item is
disabled when there are no options defined in the database.
Portfolio Navigator
The Portfolio
Navigator presents your current portfolio positions in a hierarchical
explorer-like navigator, allowing you to drill down to the positions level
within a particular stock or option, or abstract upwards in the tree until all
you can see are column totals for the entire portfolio. Subtotals are provided at each level in the
tree, i.e. the portfolio level, the instrument level (options or stocks), the
issue level (particular stock and option issues), and the position level
(issues you have a stake in). Background
colors distinguish between row types to manage display complexity. This
menu item is disabled when there are no positions in the database.
The Positions
Transcripts dialog produces a detailed text transcript of all positions closed
in a given year or currently open. It’s
the textual equivalent of a position level Portfolio Navigator display. It allows you to save the contents of the
transcript to a file, thus providing convenient tax time documentation. This menu item is only enabled when there are
positions in the database.
The Help Menu currently contains only ‘About
box’ information about NillaHedge.
This section covers various considerations common across
tools in NillaHedge, including the precision with
which numbers are stored, slight variations from the Windows’ standard behavior
for combo-boxes, and an overview of database behavior and many behaviors common
between the option and stock definition dialogs.
Many of the edit boxes you’ll encounter in NillaHedge dialogs await and/or display a numerical value. Most of these values are stored with floating
point precision (23 magnitude bits in the mantissa and 7 magnitude bits in the
exponent), producing the equivalent of 6.9 significant decimal digits. Examples of this level of floating point
precision include interest rates, dividend amounts, market prices, and
volatility.
Number of shares or options in a position and the total cost
of a position are all stored with double precision (52 magnitude bits in the
mantissa and 10 magnitude bits in the exponent), producing the equivalent of
15.6 significant decimal digits. When
either of these floating point representations is retrieved from the database
and presented in a dialog control, it may be formatted with a fixed number of
fractional digits, potentially truncating presentation of some of the
significant digits. Be assured that the
originally entered precision has not been truncated in the database,
they’re just not being displayed.
In the interest of minimizing pen taps, NillaHedge
combo-boxes operate slightly differently from the Windows standard. Suppose you’re using the drop-down portion of
the combo-box and something in it is currently selected. If you tap somewhere in the dialog outside
the drop-down box in a standard Windows application, it cancels the
selection. By contrast, NillaHedge accepts the selection.
It is useful to note that once saved, an instrument (stock
or option) definition will be retained in the database forever, so it behooves
you to limit the number of definitions you create to those that are actually
meaningful. The storage occupied by an
instrument definition is quite small, but NillaHedge
thinks that each definition is equally significant, so the symbols for any junk
definitions that may creep in will take up rows in the drop-down box when
you’re trying to locate a definition later.
Instrument definition dialogs have three things in
common. Each one has a combo-box where
you can type or select the unique symbol associated with the instrument
definition, an edit box for the instruments’ current market price, and an edit
box labeled ‘Description’ whose contents serve no other purpose than confirming
that you’ve recalled the definition you thought the symbol represented.
The Stock Definition Dialog refers to a stock symbol and the
Option Definition Dialog refers to an option symbol. The concepts are identical, but uniqueness is
instrument dependent, meaning that you can define a stock and an option with
the same exact symbol and they won’t collide with one another in the
database. You might confuse yourself by
having an option and a stock named Ford, but the database will keep them
straight. Any string of characters will
suffice as the symbol - however, using the generally accepted exchange
registered symbols have benefits discussed in the next
section.
The database locates instrument (stock or option)
definitions using the symbol you provide in the control located in the top left
area of the dialog. This control is a
combo-box, which means it has both edit and drop-down
capabilities. You can recall instrument
definitions by selecting a symbol from the drop-down box, or by a combination
of ‘typing’ and scrolling. It supports
auto-completion, so the typing required on recall is minimal. There’s no sense going to extra effort for
first letter capitalization because all symbols are forced into upper case when
the instrument definition is saved to the database.
You can use any arbitrary symbol in an instrument
definition, but there are advantages to using exchange registered symbols. For example, suppose you set up your database
using ‘AMAT’ as the symbol for Applied
Materials Inc. Later, you use the Option
Chain Retriever (in the Tools menu) to download options derived from Applied
Materials stock. In the process of
fetching option pricing and volume information, the Option Chain Retriever will
automatically update the price of Applied Materials stock. The benefit of using the exchange registered
symbol is that you can run with the preference to confirm stock price updates
disabled (in the Confirmation Options dialog), and let stock price updates sail
through without intervention. The
default is to let the stock price updates go through without confirmation.
Conversely, if you had used ‘AMAT’
to refer to Amalgamated Mining and Technologies in your database, and you
subsequently desire to use the Option Chain Retriever to get the options for ‘AMAT’
(by which the rest of the world refers to Applied Materials Inc), you could
potentially overwrite the price of your AMAT
with the current market price of Applied Materials. ‘Potentially’ enters the game because you can
require that NillaHedge confirm all stock price
updates from the Option Chain Retriever by setting a preference in the
Confirmation Options dialog, so you have the opportunity to cancel the update
if you come to your senses just before the price would get committed to the
database. Obviously, this is only a
patch on a bad situation - you have forced yourself into manually updating
prices for AMAT forever.
A similar situation exists for option symbols.
Suppose that you haven’t modified the default values of the
confirmation options and have just defined an instrument with the symbol ‘INTC’. 
When
you click the OK button in the upper right hand corner of the dialog, a
confirmation dialog like the one at left will be displayed. Screen space on the PocketPC
is precious and many of the dialogs are packed with controls, so instrument
(stock and option) definition dialogs post a small confirmation dialog, asking
you to confirm or cancel saving the changes you’ve made to the definition as a
substitute for explicitly including a Cancel button. When you initially define an instrument, it
may seem superfluous to ask if you really meant to save the definition, but
later when you’re editing a preexisting definition, the opportunity to cancel
the save may prove more useful.
If you’d rather opt out of confirmations like these, you can
use the Confirmation Options dialog to uncheck the preference labeled
‘Definition dialogs – close’. When this
preference is unchecked, subsequent close events in any of the three instrument
definition dialogs will simply update the database without asking permission.
If you’ve already detoured through the Confirmation Options,
you may have noticed a preference labeled ‘Definition dialogs – change
symbol’. This preference operates
similar to ‘Definition dialogs – close’, but is triggered by changing the value
of the stock symbol while one or more of the remaining dialog controls contains
a value different from the associated value in the database. Naturally, if confirmation is enabled and
you’ve never saved an instrument definition with that symbol before, then a
confirmation dialog will post no matter what state the controls are in.
The Option Definition Dialog is one of two
ways to create an option definition in NillaHedge. The other is to use the Option Chain
Retriever to save one of the options displayed in its options list, but we’ll
get to that later. To define an option
from scratch, you’ll need the option’s symbol, as well as its market price,
strike price, expiration date, underlying stock symbol, and of course whether
it’s a put or a call.
Refer to the Symbol / Identifier discussion in the
Instrument Definitions section.
Automated price updates depend on internet sources which
catalogue pricing information using exchange registered symbols. No confirmation option allows you to
interfere with option price updates, so it’s imperative that you stick with the
exchange registered option symbols.
Market price and strike price are currency denominated values.
The Expiry date picker captures the option’s expiration
date. The vast majority of stock options
expire on the third Friday of the month (technically the third Saturday, but
the exchanges are closed on Saturdays), so the convention is to say they expire
on the third Friday. Be careful to
specify the correct date. One could
argue that the day of the month in the expiry date is superfluous because
options always (effectively) expire on the third Friday so you’d be right
insofar as exchange registered issues go.
However, since the Option Chain Retriever will automatically save
exchange traded options directly into the database, including the exact
expiration date, we decided to leave exact date flexibility in the Option
Definition Dialog. Unfortunately, with
that flexibility you also get the burden of accurately specifying the expiry
date each time you define an option manually.
Sorry about that.
The Put / Call radio button pair is technically a
tri-state. It is initialized to an
undefined state, which prevents analysis, forcing you to choose a valid
value. You might ask, why not just
pre-select Call as the default value and save the user from a pen-click, half
of the time? Well, it’s because an
invalid default value forces the user to proactively select a valid value, thus
minimizing the potential of defining an option with an incorrect Put/Call value
as an oversight.
The Underlying Stock is a combo-box control, so you can
either type the stock symbol or pick it from a list of stock symbols already
defined in the database. If the
specified stock doesn’t already exist in the database or it has zero volatility
or zero market value, analysis will be disabled, resulting in a display like
the one on the previous page.
However, if there is an underlying stock defined in the
database with positive market value and positive volatility, the option can be
analyzed, producing analytical results like those at right.
All of the analytical information presented below the
description field also appears in the Option Analyzer. Please refer to the Glossary and the section
on the Option Analyzer to learn more about implied volatility, Black-Scholes value and greeks,
elasticity, and the probability of being in the money, p(ITM).
The Stock Definition Dialog includes controls
for entering a stock symbol, the stock’s volatility, its current market price,
a brief description, and a number of controls supporting quarterly dividends.
Refer to the Symbol / Identifier discussion in the
Instrument Definitions section above.
If you never intend to analyze options on a particular
stock, then volatility can be ignored because it’s only used to price and
analyze options derived from the stock.
However, if you are interested in analyzing options on a stock, you should
know a couple of things. First, many
sources of volatility report the volatility as a percentage, e.g. if the
volatility is 0.391, they may report 39.1%.
NillaHedge expects volatility to be the
un-scaled floating point value, not the percentage. An excellent source for volatility values
(reported as percentages) is Robert's Historical
Stock Volatilities.
The stock price obviously affects the capital
value of your portfolio, and dividends are a motive force behind income
reporting (elsewhere in NillaHedge). If you’ve done any amount of income
investing, you will have discovered that there can be several weeks between the
ex-dividend date and the issue date for the dividend check, but NillaHedge only has only one set of dates and uses the
ex-dividend date for both purposes.
There are several justifications for this
simplification. First, option valuation
is driven by the ex-dividend date not the payment date. Second, capturing eight dates associated with
dividends would substantially complicate the Stock Definition Dialog and pose a
greater data entry burden on the user. Finally,
given the limited storage capabilities of the typical PocketPC,
storing just four dates instead of eight, saves storage space. The side effect is that the current yield may
be affected. It will usually be
inconsequential.
You’ll note that the date picker controls in the Stock
Definition Dialog can specify years as well as months and the day of the
month. NillaHedge
assumes that dividends recur annually on the given calendar date, ignoring the
year specified. Each of the four
dividend date pickers is restricted to the months in the associated calendar
quarter. If a stock pays dividends just
once per year, in May, the only place you can successfully specify the date is
in the date picker immediately to the right of the Q2 checkbox. You’ll also find that the dividend date
picker and dividend amount for the Q2 dividend are disabled while the
associated quarterly checkbox is not checked.
Once you check the checkbox, the date picker and dividend amount
controls are enabled. If you later
desire to experiment with the effects of discontinuing the dividend, you need
only disable the checkbox for the associated dividend and save the modified
stock definition back to the database.
The ex-dividend date and the dividend amount are retained in the
database, but that dividend is excluded from all subsequent income
calculations. At the end of the
experiment, you can simply re-check the Q2 checkbox and re-save the stock
definition.
When a stock price and one or more quarterly dividends are
defined, the dialog will report the current yield of the dividends as a
percentage of the stock price.
Since vanilla put and call options refer to an underlying
stock, you may wonder if you must create a stock definition before creating an
option definition which refers to it.
The answer is no. If a stock
definition does not exist at the time that an option definition referring to it
is saved, a placeholder stock definition will be created for you. It will be up to you to enter appropriate
values for the market price, volatility, dividends, and description, if any. The Stock Definition Dialog is the only place
where you can enter a description, dividend dates and amounts for a stock, but
the Option Analyzer also allows you to modify the stock price and volatility
for an option’s underlying stock.
Additionally, the Option Chain Retriever will automatically update the
stock price whenever it successfully retrieves an option chain for a particular
stock.
There are two preferences dialogs in NillaHedge,
both launched from the Edit menu.
The Confirmation Options dialog allows you to view and
modify the current value of seven confirmation options which affect behaviors
in the analyzer dialogs, instrument definition dialogs, the Positions Dialog,
the Portfolio Navigator, and the Option Chain Retriever.
The Positions List Options dialog allows you to view and
modify the visibility of columns in positions lists that appear in the
Positions Dialog and the Portfolio Navigator.
There are three groups of preferences in the Confirmation
Options dialog. Each preference controls
whether to require user confirmation before doing something irreversible to the
database. The first group controls
whether to confirm instrument (option or stock) definition updates. The second
group controls whether to confirm portfolio position modifications and
deletions. The third group just controls
whether to confirm stock price updates in the Option Chain Retriever.
The second and fourth check boxes indicate your desire to
have NillaHedge post a confirmation dialog before
updating an instrument definition when you close the dialog. The second check box affects close events in
the Option Analyzer and the fourth check box affects close events in the
instrument definition dialogs. The
default value for both preferences is to require confirmation.
The first and third check boxes indicate your desire to have
NillaHedge post a confirmation dialog before updating
an instrument definition when you change the symbol (identifier) in one of the
instrument definition or analyzer dialogs.
The first check box regulates change symbol behavior in the Option
Analyzer dialog. The third check box
dictates change symbol behavior in the instrument definition dialogs. The default value for both preferences is to
require confirmation.
The preferences in the second group affect whether you’re
queried for confirmation after pressing the Delete or Modify buttons in the
Positions dialog. Confirming position
deletes is probably a good idea, but it’s not a huge tragedy if you don’t
confirm modify operations, because you’ll have the opportunity to re-Enter the
position before quitting the Positions Dialog, but no warning will post when
you close the dialog with values present in the controls above the Enter
button. The default value for both
preferences is to require confirmation.
The preference in the third group merely puts you in the
loop before the stock price can be updated by the Option Chain Retriever. Its default value is false, in the hope that
you will wisely use exchange registered stock symbols, making such
confirmations superfluous.
You might wonder, if there’s a
preference for confirming stock price updates in the Option Chain Retriever,
why not do the same for option price updates?
First, the two types of price update don’t generate the same amount of
user interaction. There is only one
stock price per ‘Fetch’, so there would never be more than one confirmation
posted on its account. In contrast,
there might be a half-dozen or more options defined in your database that might
need to have their prices updated as a result of a single ‘Fetch’. The criteria used to decide whether to update
the option price is that an option definition exists, not whether it would
affect your portfolio value (i.e. all definitions will attempt an update, not
just those with associated positions).
As a result, it could get really irritating working through
all of those confirmation dialogs, so additional logic would be required to
manage possibilities like, ‘No, to all’, ‘Yes, to all’, ‘Abort’, etc. All of that complexity to prevent updates to
option definitions that might have been defined with an exchange registered
symbol, but didn’t represent the issue referred to by the registered
symbol. It further requires that you’d
recognize that the symbol you used for your special option now collides with an
exchange registered option. Ultimately,
it seemed unlikely that the same user that would unwisely pick an exchange
standard symbol to represent something other than the normally associated
option would subsequently recognize that it was being inappropriately
updated. In short, we believe that
option price update confirmations would probably never get used, so the
opportunity to prevent automatic updates is not offered.
We therefore strongly recommended that you stick with
exchange registered option symbols to define options that the rest of the world
associates with those symbols.
Positions List Options are virtually
self-explanatory. The preference names
correspond with columns in the Positions dialog and the Portfolio
Navigator. The preferences in the left
column affect the visibility of columns in the Positions dialog and the
preferences in the right column affect the visibility of columns in the
Portfolio Navigator.
All of the preferences have the default value of enabled
(checked), so all columns will be visible in each of the affected dialogs. The columns appear in the same order that
they occur in the preferences list at right.
The only preference that doesn’t coincide with a column
heading is the very last one on the right – ‘Initially Hide Positions’. The Portfolio Navigator has many row types;
the row type at the leaf level in the hierarchy displays a position in a format
almost identical to the display used in the Positions dialog.
The justifications for a default
of initially suppressing the display of positions went something like
this. 1) Positions are always displayed
in the Positions dialog. 2) You have the
option of expanding an issue’s summary node to see the positions that
contribute to that subtotal row. 3)
Portfolios would require more scrolling if the positions were visible. 4) It would be quite a bit of work to toggle
all of the issue expansion nodes off, to facilitate fitting more summary
information onto the small screen.
There are three dialogs in NillaHedge
that deal with positions, the Positions Dialog, the Portfolio Navigator, and
the Positions Transcripts dialog. The
Positions Dialog offers the opportunity to view or create the positions linked
to a specific stock or option issue.
The Portfolio Navigator provides a top-down view of the
entire portfolio, optionally expanding or collapsing branches in the hierarchy
down to individual positions at the leaf level.
The Positions Transcripts dialog provides a text transcript
equivalent to the leaf level in the Portfolio Navigator. The intent is to export these journal
entries for review, tax records, and other documentary purposes.
The Positions Dialog is where all positions in your
portfolio are created. NillaHedge tries to anticipate which instrument type you’ll
want to create positions for. If you
haven’t defined any options or stocks, NillaHedge
won’t be able to guess an instrument type, so it will initialize the Positions
Dialog with the Symbol combo-box disabled and no selected value in the radio
button group as shown above.
However, if you have defined some
instruments, NillaHedge will select an instrument
type based on the type you last defined, created a position for, or
analyzed. For example, if you just
defined a stock, the Positions Dialog will choose Stock in the radio button
group and load the known stock symbols into the combo-box. In the next screen shot, we’ve selected Intel
Corp (INTC)
from that list and filled in values for Units
Note that all of the buttons that operate on the positions
list (Enter, Modify, Close, and Delete) are disabled for an issue with no
positions.
When the instrument type radio button group is set to
Option, the symbol combo-box selects option symbols. When the group is set to Stock, the symbol
combo-box selects stock symbols.
Note that it’s not necessary to select a
symbol from those already defined in the database. If you enter a new symbol, a placeholder
instrument definition will be created for you, though NillaHedge
will not make any assumptions about the issue’s current market price (e.g.
based on the number of units purchased and their total cost). Using zero as the market price in the
placeholder definition serves as a reminder that its value has never been set.
The current date is used as the default value for the
Purchase date, but future dates are disabled, so it’s not possible to enter pro
forma positions.
The number of units (options or shares) in a position is
stored as a double precision floating point number. While fractions of an option don’t find much
practical 
application, stock reinvestment plans often
produce fractional shares of stock, hence the floating point
representation. For short sales, specify
the number of units as a negative number.
Please note that the unit of 
measure for an options position is one
option, not a contract consisting of 100 options. For example, if you buy 3 option contracts,
you would enter 300 in the Units edit-box.
Total Cost is also stored as a double precision floating
point value. The presumption is that it
represents the cost of the position including any transaction fees. Note that the cost associated with a short
sale should be negative, thus representing an inflow of capital after expenses.
As an example, if you chose INTC
as the stock symbol and enter 100 as the number of shares, the dialog
calculates and enters the cost of the position based on the market price of INTC,
as currently defined in the database. No
fees are added at this point (that’s left for you to do manually). We’ll set the date back a year and add $100
to the total cost.
The Stock/Option radio button group
controls which symbol table is loaded into the Symbol combo-box.
The Note field is provided to document almost anything you’d
like to associate with a position.
When the Option/Stock Radio Button Group is set to Option, a
string is pre-loaded into the Note box describing the current option in the
symbol selector. The string includes
exchange symbol for the option’s underlying stock, the option’s expiration
date, whether it is a Put or Call option, the option’s strike price, and the
option’s current market price. An
example for the ANQGC.X is shown above right.
Its underlying stock is Applied Materials (exchange symbol AMAT);
it is a July 2008 Call option struck at $15; and its current market price is
$4.40.
Once a symbol has been
entered and there are values for the number of shares and the total cost, the
Enter button will be enabled. As soon as an entry appears in the position
list control (below the Enter button), the position has been saved in the
database. Closing the dialog only
discards the contents of the fields (above the Enter button) used to create a
position.
The position has been committed to the database and a row is
added to the positions list for INTC to
depict the current state of the database.
Note that the number of shares and the total
cost fields now contain zeroes, the Note field has been cleared and the Enter
button has been disabled.
Since INTC
was defined previously with a market price of 27.33, the market value of the
position reflects the number of shares times the market price of the
stock. If we scroll to the right in the
positions list, we can see some of the remaining columns in the list
control. Since we added $100 to the cost
of the position, the Capital Gain shows a loss of $100. INTC pays
a $0.24 dividend once annually, so 100 shares of dividend income is displayed in the Income column. The Net Gain column merely sums the Capital
Gain and Income column entries and the ‘% Yield’ column annualizes the Net Gain
over the holding period.
If we scroll to the right, we can see the Note we entered
above as our source of funds.
Let’s see what happens when we add another INTC
position. We’ll change the date and buy
200 shares for $5366, including transaction fees, and note the purchase as
being financed by a haul in a Bingo game.
As before, the Enter button becomes disabled, the Note is
cleared, and the Units and Total Cost fields are zeroed out. The Positions List now shows the following
contents:
The ‘Bingo haul’ position has become the topmost position,
showing a positive Net Gain and annualized yield. Obviously, positions need not be limited to
outright purchases, they can just as easily be the
result of dividend reinvestment.
A Total row, highlighted in cyan, has been added to depict
the sums for each of the columns - the exception being the ‘% Yield’ column –
this Total row entry is the cost weighted average annualized yield of the
contributing positions, so you can get immediate feedback on how well cost
averaging is working for you. The total
row is only visible when more than one position exists for the issue you’ve
selected.
Positions List Columns
Column headings are generally self explanatory, so we’ll
focus on a few things that may not be as readily apparent. First, the list control supports column
resizing, reordering, and sorting (toggles between ascending and
descending). If a total row is present,
it is not included in the sort. Stocks
with dividends generate income, so there’s a column displaying income when the
radio button group selects Stock. The
Net Gain column displays the sum of the Capital Gain and Income columns and is
also only displayed for stocks. When the
radio button group selects Option, you’ll find another column (assuming its enabled) just to the left of the Note column displaying
the exercise value of the position.
You’ll note that the second column (when the Purchase Date
and Options/Shares preferences are both enabled) changes its name to reflect
what sort of units the position represents.
Managing Display of the Positions List
Clearly, you can’t see the contents of all columns without
scrolling the Positions List horizontally, but you can disable the display of
any of the columns in the Positions List Options dialog, thus reducing the need
to scroll horizontally.
Managing the Contents of the Positions List
The three buttons below the Positions List allow you to
manage the list of positions displayed above.
If you select one of the positions in the list, you’ll see the row
highlight and the three buttons at the bottom of the screen become
enabled. You may notice that you can’t
select the total row – it’s not a real position, just a summary entry in the
list control.
Here’s what happens when you select one of the three buttons
at the bottom of the dialog.
Delete
The Delete button is the simplest of the three. Selecting it causes the message box at right
to post over the dialog. If you click ‘Yes’, it will disappear from the
database forever. The Delete button is
the only one of the three bottom buttons that supports multiple selections.
Modify
The Modify button is very much like the Delete button, in
that it warns you that you are about to delete the selected position, and once
you select ‘Yes’, the position will be permanently deleted from the database,
just as it promised. The difference is that Modify overwrites,
without asking permission, all of the fields in the dialog with values taken
from the position you are ‘modifying’.
Clearly, 
you shouldn’t use the Modify button if you
have typed information into the fields above the Enter button that you care
about.
After you complete your modifications, you must re-Enter the
position in the database. Until it
appears in the Positions List below the Enter button, it’s not saved in the
database – that’s why the warning message says “you are about to permanently
delete the selected position” when you just selected Modify.
Close
The Close button also has irreversible consequences, but it
does not have an associated preference in the Confirmation Options Dialog
because it needs to capture additional information along with your approval to
proceed. The Close Position Dialog
completely overlays the Positions Dialog and collects three things from you
which enable converting it into a closed position. The date the position was closed, the net
proceeds from the sale, and a closing note.
The closing date can be no later than the current date. Upon selecting the ‘OK’ button, a ‘closed
position’ is created in the database with all of the information previously
associated with the active (open) position;
the active (open) position is then deleted.
By design, there is no mechanism for modifying a closed
position – it can’t be deleted, modified, or converted back into an active
(open) position, but you can get transcripts of all closed positions according
to the year in which they were closed (see the Positions Transcripts Dialog on
the Tools menu).
The Portfolio Navigator is the second positions dialog in NillaHedge. It
differs from the Positions Dialog in that it doesn’t allow you to close,
delete, enter, or modify positions in your portfolio. Its purpose is to display positions and
summarize your portfolio at various levels.
The hierarchical display implements a folding spreadsheet whose branches
can be expanded to obtain more detail or collapsed to a summary. The example at right depicts a portfolio
containing positions in three Applied Materials options (ANQBC.X, ANQBE.X, ANQBR.X),
one Intel option (NQGX.X), and two stocks (Ford and Intel). The position rows are initially 
invisible, so all you see at right are the
issue summary rows and the total row for all bonds in the portfolio.
If you click on the
icon next to the symbol (identifier), individual positions
will be displayed above the issue’s summary row. For example, if you expand the ‘F’ and ‘INTC’ branches in the example above, you’ll get 
the
display at left. Note that position rows
always appear above the issue’s
summary row, as you might do if you were tallying the positions for each
issue. To collapse a branch, just click
on the issue’s summary row
icon.
The summary rows
for the Options folder and the Stocks folder have manila backgrounds,
symbolizing manila folders. Position
rows have a powder blue background - hopefully alliteration will serve as the
mnemonic there. The portfolio summary
row and issue summary rows and use a plain white background.
Columns
The Portfolio Navigator treats columns slightly differently
than the Positions Dialog. The columns
available are Date/Name, Units, Cost, MktValue, CapGain, Income, NetGain, %
Yield, ExerVal, and Note/Desc. Dividend income contributes to the net
gain. Net gain is the basis of the
annualized yield calculation.
NetDate/Name and Note/Desc columns present information which depend
on the row type. Position rows, display
the purchase date in the Date/Name column and the Note you entered when you
created the position in the Positions Dialog in the Navigator’s Note/Desc column.
Issue summary rows display the issue’s symbol in the
Date/Name column and the description you created in the instrument definition
dialog in Navigator’s Note/Desc column. Columns can be reordered using tap and drag,
but sorting is not currently available.
You can use Positions List Options to prevent some columns from being
displayed. The default is for all
columns to be visible.
In this example, the annualized yield for the portfolio as a
whole is 6.405%.
Note: Purchase prices
and dividend rates in this example are entirely fictional.
The Positions Transcripts dialog collects information for
all open positions or for all positions closed within a given calendar year and
presents a textual report summarizing the activity. Of course, they are
useful as journals at tax time, but transcripts also serve as a faster means of
reviewing the current state of capital gains, coupon income, annualized yields,
etc. because scrolling a plain text window is faster than scrolling a list
control and you can see the derivative data all at once so you don’t have to
scroll right and left to get a picture of what’s going on.
The ‘Year Closed’ combo-box allows you to choose between
‘Open’ and any years for which closed positions exist. If there is only one year, e.g. all positions
are active (open) or all closed positions were closed in the same year, then
that year’s positions will be loaded by default. If there are open and closed positions, Open
positions will be loaded by default.
Otherwise the most recent year’s transcript will be loaded by default.
In the example above right, you can see the
first two journal entries from the list of open positions. Each entry
includes: an opening date, the number of shares or options purchased, the
stock or option symbol, the description associated with the issue, the total
cost of the position, any note you may have created with the position, and
derivative information including capital gain, income, net gain, and the
annualized yield represented by the net gain.
Dividends from the purchase date to the present date contribute to
income figures. Portfolio totals for
cost, capital gain, income, and net gain are posted below the positions listed
in the transcript. The cost weighted annualized yield of all positions in
the transcript completes the picture.
A transcript containing one closed positions is shown at
right. It adds the closing date and closing note entered at the time the
position was closed to the information associated with an open position.
The transcript displayed is not saved to a file until you
choose to do so manually.
The ‘Save Transcript’ button allows you to
save the transcript to a file, for review and editing outside NillaHedge and subsequent upload to a desktop
computer. The file dialog shown below is posted after clicking the Save
Transcript button. It allows you to save the transcript to the file name of
your choosing.
The
Positions Transcripts dialog traverses the database differently than other
tools in NillaHedge. Other NillaHedge
tools access positions through the instrument (stock and option) definitions,
since each tracks its own list of positions.
Positions
transcripts are generated by bypassing all of the instrument definitions and
directly accessing the portfolio positions. This approach has both
tactical and strategic advantages. From a tactical perspective, it saves
CPU time (something that should always be conserved on a Pocket-PC platform)
which might otherwise be wasted inspecting instrument definitions that don’t
have associated positions.
From a strategic perspective, directly accessing
the portfolio positions enhances robustness by potentially salvaging position
information from a partially corrupted database. Hopefully, you’ll never
have to find out whether this capability actually saves your bacon or not.
The
downside of initially bypassing the instrument definitions is that positions associated
with a particular issue won’t necessarily be contiguous in the
transcript. The order in which the journal entries appear is generally
the order in which you created the positions, except that space occupied by
closed and deleted positions is recycled by subsequently created
positions. For example, if you create twenty positions in your portfolio
before deleting the second one ever created and then create a new position, the
new one will appear second when you generate an open positions transcript.
Given the benefits of efficient CPU utilization and the potential to salvage a
corrupt database, journal entry disorder was viewed as a reasonable
inconvenience. Tax agencies care more about completeness than order, and
that’s what the transcript is intended to address.
The Option Chain Retriever downloads option
pricing and related information via the internet. It captures a chain of options expiring on a
given date and loads up the Option Chain list control, one row for each option.
It automatically updates the price of any option in your
database found in a downloaded chain, but won’t create any new option
definitions automatically. It’s very
important to stick with exchange registered option symbols because the price
update process doesn’t allow the user disapprove or otherwise bypass price
updates.
The Option Chain Retriever will also silently update the
price of the underlying stock, unless you set the Confirm Save Preferences to
require user confirmation. If
confirmation is required, the Option Chain Retriever will post a confirmation
dialog before modifying the stock price.
The Option Chain Retriever is initialized with no stock
symbol and both buttons disabled.
The Stock Symbol is a combo-box, supporting
drop-down and edit modes of input. You can either select the symbol for a stock
you already have defined in the database via the drop-down box, or use the
Input Panel to type a stock symbol not yet in your database. We entered ‘AMAT’
in the example at right. Once a symbol
is available, the ‘Fetch’ button becomes enabled.
Note:
There is no local cache of valid stock exchange symbols in NillaHedge
- the server is the arbiter of validity for stock symbols. Since it takes a few seconds to hear back
from the server, you’ll be more productive if you avoid fetching invalid
symbols.
Once enabled, clicking the Fetch button will initiate a
connection with the server to retrieve an option chain with the earliest
possible expiration date for the company represented by the Stock Symbol. In the example above, we entered ‘AMAT’
to retrieve the options for Applied Materials Inc (whose Nasdaq symbol is ‘AMAT’). The Fetch button is disabled as soon as the
download is launched.
After clicking the Fetch button, a series of
messages will appear in the status line at the bottom of the dialog (to the
left of the ‘Save to DB’ button). The
first status message is ‘Opening Request…’ letting you know that progress is
underway. Opening a request is a local
operation and should complete very quickly.
If this message is still around after more than a second, it’s likely
that your internet connection is down.
The second status message, ‘Sending Request…’ indicates that
NillaHedge is attempting to negotiate a connection
with the server. Obtaining an initial
connection can sometimes take three to five seconds, depending on the quality
of your internet connection and the demand on the server, but once a connection
has been established, subsequent requests generally proceed with sub-second
elapsed times.
The third status message, ‘Downloading…’ indicates that a
connection has been successfully established and the data is currently being
copied from the server onto the PocketPC. Downloading can also experience variations in
completion times, from less than a second to a couple of seconds, depending on
the speed and quality of your connection.
The fourth status message, ‘Extracting…’
occurs during the phase where the list control is being populated with the
information just retrieved. Here, the
total elapsed time is entirely dependent on how fast your processor is and how
many options are contained in a single options chain. For a stock with a dozen options, the
extracting phase completes almost instantaneously, but it may take a couple of
seconds to populate the list control if there are hundreds of options in a
single download.
When the extraction phase completes, the status line
indicates the number of puts and calls currently contained in the options list;
the options list contains a row for each of the options found, the stock price
and company name are displayed below ‘Stock Symbol’; and the Expiry combo-box
has been loaded with all known expiration dates for options on the specified
stock symbol.
The first result of extraction is the display of the company
name and the current stock price associated with the symbol you requested
options for. There’s nothing magical
here. The stock price is delayed by
about fifteen minutes from the current market.
The company name is provided so you can verify that you received what
you intended to retrieve.
The next result of a successful download is that the Expiry
combo-box is loaded with the known expiration months for options on the
specified stock. Immediately after
download, the Expiry combo-box displays the nearest term expiration date
available. Subsequent expiration dates
can be found in its drop-down box.
The Expiry combo-box serves two purposes. If you select a date for which you have
previously downloaded options, the Expiry combo-box will restore the original
sort order (if it has been modified) and scroll the options list so the first
option matching the selected expiration date occupies the first row of the
options list.
If you select a date for which you have not previously
downloaded options, the Expiry combo-box will just enable the Fetch button,
enabling you to retrieve options with that expiration date into the options
list.
The primary result of extraction is an option chain
populating the central list control with columns indicating whether the option
is a put or a call; its strike price; expiration month; option symbol; a set of
prices (or derivative numbers): Last, Change, Bid, Ask; Volume, and the Opening
Interest in the issue.
Highlight Color
Rows in the options list are color coded to indicate whether
the option is a put or a call (making the first column redundant). Puts are highlighted in plum, while Calls are
highlighted in cyan.
Column Sorting
All of the column headers act as sort buttons on the
column. The first click is an ascending sort, the second produces a descending sort. The result of an ascending sort on Strike
price is shown at right.
After sorting, it may be desirable to return to the original
sort order. Since there’s nothing
intrinsic about the option pricing data that would allow a sort on the data
that would restore the original order, the original sort order is hidden in the
empty column after the Opening Interest column.
Its column header button (only about two characters wide) is blank, but
it sorts using the list control’s original sort order.
The ‘Save to DB’ Button is enabled whenever one or more rows
are selected, even if the selected row doesn’t currently appear within the
viewable area, i.e. when you select a row and subsequently scroll the
window. You can click, drag, and release
to select a screen full at a time, or if you use a real or the builtin soft keyboard, you can use shift-click and
control-click to add or subtract rows from the selected list.
When you click ‘Save to DB’, the selected options are
immediately saved to the database.
Shortly thereafter, the rows will automatically be deselected,
indicating completion of the operation.
When the rows are deselected, the ‘Save to DB’ button will be disabled
too.
The option definitions saved will be complete, even if you
haven’t previously defined the underlying stock in your database. But if that is the case, the stock will not
have dividends defined and it will have a default value for the stock’s
volatility. It’s wise to set dividends
to accurate values because they affect the value of options drawn on that
underlying, as well as all of the income calculations in the positions dialogs
and the positions transcript.
The Option Analyzer dialog enables you to
experiment with values for the risk free rate, option price, stock price, and
stock volatility to better understand an option’s sensitivity to changing
market conditions. There is a subtle
difference in the way that the Option Symbol combo-box works vs. how that
control works in the Option Definition Dialog, so we’ll address that
immediately.
The Option Symbol combo-box in an analyzer dialog doesn’t
allow you to create a new symbol as you can do in the Option Definition Dialog. All you can do is select one of the
preexisting option symbols. Given that,
we decided to always load the first option symbol found, so you instantly have
meaningful output to review when you open the Option Analyzer.
The Option Price edit box is a window on the database’s
stored value for the option price. If
you change the option price here, the new value will be saved in the option
definition when you change option symbols or quit the dialog. If you have the appropriate save confirmation
preferences enabled, either of those actions will cause a confirmation dialog
to post asking permission to update the database.
Immediately below the Option Symbol combo-box, you can see
several items that summarize the option definition. The expiration date, whether it’s a put or a
call, the strike price, and the symbol of the underlying stock (surrounded by
dashes). In the example above, we can
see that ANQAE.X is a call option on Applied Materials Inc. (NYSE symbol = ‘AMAT’),
struck at 25.0, expiring on 18-Jan-2008.
The Stock Volatility edit box is a window on the database’s
stored value for the underlying stock’s volatility. If you change the volatility here, the new
value will be saved in the stock definition when you change option symbols or
quit the dialog. If you have the
appropriate save confirmation preferences enabled, either of those actions will
cause a confirmation dialog to post asking permission to update the database.
The Stock Price edit box is a window on the database’s
stored value for the underlying stock’s market price. If you change the stock price here, the new
value will be saved in the stock definition when you change option symbols or
quit the dialog. If you have the appropriate
save confirmation preferences enabled, either of those actions will cause a
confirmation dialog to post asking permission to update the database.
The Risk Free Rate edit box displays the currently stored value
for the risk free rate of interest. It’s
expressed as a percentage with a default value of 3%; here 4.76% is used. The risk free rate can be computed in the YieldCurveFitter (a separate tool) or you can set it
manually here. It’s a crucial quantity
in valuing options, also used in numerous other NillaHedge
tools. If you have created option
positions and you want a realistic assessment of the value of those positions,
you should always review and possibly modify the value of the risk free rate in
the Option Analyzer, in one of the Explorer dialogs, or by using the Yield
Curve Fitter prior to valuing any option positions.
Black-Scholes Value
The Black-Scholes value is
discussed in the Glossary, so we won’t review the details here – it’s an
analytical solution to option valuation that accounts for the current price for
the underlying stock, its volatility, and the risk free rate of interest. Variations on the theme account for discrete
dividends or model dividends as a continuous yield. NillaHedge discounts
the stock price with the present value of any dividends rather than resorting
to a continuous yield approach. This
seems to model market behavior more effectively than the continuous dividend
yield model, especially for options with expirations less than one year.
Implied volatility is defined in the Glossary, so we won’t
delve deeply into it here, but briefly volatility represents the standard
deviation of returns on the underlying stock over a year. Volatility is a crucial quantity used to
assess option value and because of that role, it can be estimated given the
other market conditions, namely the current value of the risk free rate, the
current market price of the underlying stock, and the current market price of
an option on that underlying stock.
Volatility is best estimated using options which are at or near the
money and not overly distant from expiration.
Options that are far from the money and/or greater than a year from
expiry tend to incorporate secondary risks not accounted for in nearer term,
nearer the money options. Both
situations usually result in pushing the implied volatility higher than stock
returns warrant. It’s relatively rare to
see a near term volatility higher than longer term volatilities.
iV Pricing Error
Calculating implied volatility is an iterative process,
which may fail to converge on a satisfactory solution. The degree to which a solution is
satisfactory is given by the pricing error associated with the implied
volatility. Ideally, this should be a
vanishingly small number, as close to zero as possible. When the implied volatility pricing error is
negative, it means that the implied volatility produced a market price lower
than the specified market price for the option.
Conversely, when iV pricing
error is positive, it means that the implied volatility produced a market price
above the specified market price.
When the option is ‘rationally’ priced, implied volatility
will generally converge and produce little or no pricing error. So pricing error can be an indication that
options are incorrectly priced. The only
way to know for sure is to look at the relationship between put and call prices
at the same strike. The market is
correctly pricing options when the following relationship holds: 
, or more accurately 
, where C is the
call price, P is the put price, S is the stock price, and 
is the present value
of the common strike of the put and the call, where 
is the time to expiry
in years. A deviation from equality is
an indication that an arbitrage opportunity exists.
Unfortunately, irrational prices aren’t the only situation
that might prevent convergence. When the
time to expiry is relatively short and the option is at or near the money (the
underlying stock price is very close to the option’s strike price) the
volatility surface will be very steep, so implied volatility will have
difficulty settling. The implied
volatility calculator detects situations involving mispricing
and instability and bails out early, indicating the smallest pricing error
found among the volatilities tested. It
doesn’t communicate why it bailed out, but if expiry isn’t near at hand and the
option is not near the money, you should consider the possibility that the
current option price represents an arbitrage opportunity. Black-Scholes isn’t
a perfect model of market behavior – some researchers have estimated that
options prices vs. their associated Black-Scholes
value typically differ by 2% or more, but an implied volatility pricing error
greater than that should definitely cast doubt on the implied volatility
reported. We considered simply clearing
the volatility or reporting “~” in these cases and not bothering to report the
pricing error at all, but ultimately decided to keep the user in the loop,
since the 2% figure itself is somewhat open to debate.
Black-Scholes
Greeks
Briefly, the Black-Scholes
greeks indicate the option’s sensitivity to changes
in the risk free rate (rho(r)), the passage of time (theta), as well as the underlying stock
price (delta), dividends (rho(D)), and volatility (vega). Derivative information includes gamma, elasticity, and the probability of closing In-The-Money (p(ITM)).
Each of the Black-Scholes greeks and derived quantities are discussed in the
Glossary.
BS CheckBox
The BS (for Black-Scholes) check box in the lower left corner allows you to see what
elasticity would be if scaled by the option’s market price (unchecked), rather
than its Black-Scholes value (checked). It is always checked when the OptionAnalyzer is first posted since that represents the
true expression for elasticity. In this
example, the gap between market price and Black-Scholes
value is substantial, so the elasticity also changes substantially.
Black-Scholes Shortcomings
It is quite unusual for such a large gap to exist between
the market value and the Black-Scholes value for an
option with only four months to expiry.
In this example, you get the same valuation whether Applied Material’s
$0.11 dividend (with ex-dividend date 14
August 2007) is entered in the Stock Definition or not, but this is
just one potential source of valuation error.
We addressed volatility mispricing earlier –
note that vega is substantial here, so under or over-estimating
of the volatility in a small way will produce large deviations away from the
option’s ‘true’ market value. At this
point in time, Applied Materials has almost doubled in price in twelve months,
so opinions regarding its volatility tend to run towards the high side.
Early Exercise Premium
Another source of error is built into Black-Scholes itself – it derives from the fact that Black-Scholes assumes that options can only be converted to stock
or cash on the option’s expiration date, so called European style options. In contrast, traded options generally allow
for exercise on any date up to and including the expiration date, so called
American style options. In efficient
markets, it is generally suboptimal to early exercise a call, but puts on
underlying stocks that don’t pay dividends can deviate sufficiently from the
Black-Scholes value to make early exercise a good bet
(capture profits now with relatively low risk of the underlying stock dropping
further than the time value of money now invested elsewhere. Over a short period, this is likely to be a
very small premium, but it grows with distance from expiry. Unfortunately, there is no closed form
solution for the early exercise premium with an arbitrary exercise date. Closed form solutions exist for what are
called Bermudan style options – options that can be exercised on one of several
dates specified in the contract. Assessing
the premium typically requires a multivariate combination of Bermudan valuations
or a much more time consuming binomial expansion - a sort of discrete time
approximation that produces better and better accuracy as the binomial tree
populates price-time space. Trading
firms with massive computer power evaluate as many as 10,000 node binomial
trees in order to accurately determine option value, including any early
exercise premium. Therefore, it should
not surprise you to find market prices in excess of the Black-Scholes value, but Black-Scholes
establishes a very reasonable low water mark, what might be considered to be
the option’s blue book value (assuming you got the volatility right). As you gain experience, you will get a sense
for how the early exercise premium scales with time to expiry.
The Hedge Explorer provides a graphical
environment in which option spreads and hedges can be evaluated. The Hedge Explorer supports analyzing
strategies involving up to three different options and their underlying stock. The quantity of each issue is user-specified,
so the Hedge Explorer inherently supports ‘ratio spreads,’ where the quantities
can take on values other than 0 or 1.
Applied Materials (AMAT)
has 50 calls and 50 puts. If you
downloaded all of them in the OptionChainRetriever,
how many spreads can you construct in HedgeExplorer? If you select a different symbol for O1, O2,
and O3, there are 
= 161,700 unique combinations, not including variations you
can introduce by adding stock to the mix, modifying your buy/sell strategy, or
using quantities other than 1. The point
is … as much
fun as it might be to scan through the profit profiles of possible option
spreads, watching plots flash on the screen, it’s just not practical to
manually review every possibility.
However, a little planning will go a long way to reducing the number of
alternatives worth considering.
The Plot
Hedge Explorer plots show stock prices along the X-axis and
profit (loss) along the Y-axis. The
colors assigned to option symbols are red, green, and blue ordered from topmost
symbol to bottom (e.g. VPJAF.X – red, ANQMC.X – green, etc. in the screenshot
at right). A stock position will plot in
purple. When two or more issues have
nonzero quantities, the sum of the positions is displayed in black. The curves are plotted in the following
order: red, green, blue,
purple, black.
To illustrate, we’ll
explore a few examples. The two options
contributing to the spread above right are (in red) ANQAT.X, an
20-Jan-06 Call struck at
$19; and (in green) ANQMD.X, a 20-Jan-06
Put struck at $20). ANQAT.X is selling
for $0.80 and ANQMD.X is selling for $2.20, so it would cost $300 plus fees to
place this bet. This combination of
options is known as a vertical (both options expire on the same date) long
strangle (nearly a straddle). If AMAT moves up to $22
before much time passes, the position produces a $100 profit, at $27, it
turns into a $500 profit.
Players on a tight budget might be happier with the spread
at right. The two options contributing
to this spread are (in red) VPJAF.X, a 19-Jan-07
Call struck at $30; and (in green) ANQMC.X, a 20-Jan-06 Put struck at $15). VPJAF.X is selling for $0.15 and ANQMC.X is
selling for $0.20, so it would cost $35 plus fees to place this bet. The call expires a year later than the put,
so upside profit potential is available for an additional year. This long strangle calendar spread is optimal
when you’re long term bullish, but have some bearish reservations for the short
term. It yields ~$240 at $27; AMAT
needs to hit $32 to produce a $500 profit.
As expiry approaches, much of the lift in the options will have eroded
away due to time-decay. You can explore
this effect in the Time Decay Explorer or by modifying the evaluation date.
If you can flash more cash, you could consider the spread at
left. ANQJP.X is a 21-Oct-05 Call struck at $14, ANQMT.X is a 20-Jan-06 Put struck at $19, and
ANQDE.X is a 21-Apr-06 Call
struck at $25. ANQJP.X is selling for
$3.40, ANQMT.X is selling for $1.55, and ANQDE.X is selling for $0.15, i.e. the
position would cost $665 plus fees. In
this case, AMAT need only move up to $24 to
produce a $5+ profit per option.
Since this is a calendar spread, it’s useful to
consider how the position behaves when the upside heavy lifter (ANQJP.X)
expires. In the screenshot at right, the
evaluation date has been moved up to 21-Oct-05
… ANQJP.X has flat-lined so the most likely portion of the upside is now under
water.
If you have a taste for arbitrage, you could play the
options and stock markets against each other.
In the screenshot at left, ANQJM.X is a 21-Oct-05 Call struck at $11, selling for $5.5 and
ANQDX.X is a 21-Apr-05 Call
struck at $22.5, selling for $0.25. The
short sale of AMAT produces $1810 (less
transaction fees) - more than enough to finance the purchase of ANQJM.X and
ANQDX.X for $575 (plus fees). Presuming that
trading costs won’t erode the $1.25 or so in per share profits, you should sell
as many blocks of AMAT as you can hedge with
purchases of ANQJM.X and ANQDX.X.
Now that you’ve seen a few ways to find a profitable
position in the Hedge Explorer, we can address the operational details.
Stock Symbol (Stk)
The Stock Symbol combo-box (to the left of the label ‘Stk’) allows you to enter or select a stock symbol from a
drop-down list. Upon picking a stock,
option symbols for that stock are loaded into the option symbol combo-boxes, so
you are always selecting options drawn on that underlying. To plot, the Stock Qty must be nonzero and its Buy or Sell button must be selected.
Option Symbols (O1, O2, O3)
Option Symbol combo-boxes allow you to select an option symbol
from the drop-down list or type a few letters and let auto-completion find an
option symbol for you. To see a plot of
an option’s profit (loss) line, the associated Qty must be nonzero and its Buy or Sell button must be selected.
Quantities (Qty)
These edit boxes specify non-negative floating point
quantities of the Stock or Option symbol to the right. ‘1’ represents a single share or option, not
a block of 100 shares or a contract with 100 options. Don’t get too caught up in the magnitudes -
for analytical purposes the ratios between the quantities are more important.
Buy/Sell Buttons
Initially in an undefined state, once selected, the Buy/Sell
buttons subsequently act as radio buttons, selecting one, deselects its
opposite.
Evaluation Date (Eval Date)
The Eval Date picker drives the
time to expiry of the options enabled in the plot. It is initialized to the present date, but
you can modify the evaluation date to see how the profit (loss) curves look at
other points in time.
Stock Price (Stk$)
The stock price is loaded from the database when a stock
symbol is selected, so you can see and modify it. The Hedge Explorer adopts the Confirm Save
Preferences of Analyzer Dialogs, so the Hedge Explorer may ask permission
before updating the stock’s market price or do so silently, based on the state
of ‘Analyzer dialogs – close’ preference.
Volatility (Sigma)
The stock’s volatility is loaded from the database when a
stock symbol is selected, so you can see and modify it. The Hedge Explorer adopts the Confirm Save
Preferences of Analyzer Dialogs so it will ask permission before updating the
stock’s volatility if ‘Analyzer dialogs – close’ preference is checked.
Risk Free Rate (RF%)
The Hedge Explorer loads the currently stored value and
displays it as a percentage. Changing
the value in the edit box will force a redraw with the new value, but the
global risk free rate won’t be updated until the HedgeExplorer
closes. At that time, the stored value
of the risk free rate is updated silently.
The Rate Sensitivity Explorer provides a graphical view of
how options behave when interest rates change.
After gaining some familiarity with the Rate Sensitivity Explorer,
you’ll probably discover that call options (NQGW.X & VNLAX.X) increase in
value when interest rates rise, while put options (INQSF.X & NQOC.X) gain
value as rates fall.
The Plot
The X-axis depicts prospective risk free rates of interest,
so all curves will pass through (rfr, 0). The Y-axis depicts the percentage change in
the value of the issue (or portfolio) at each X-value. The colors assigned to the curves are red,
green, blue, and purple ordered from topmost symbol to bottom, e.g. NQGW.X –
red, VNLAX.X – green, etc. as shown in the screenshot at left.
Plot Enabling Checkboxes
The four checkboxes on the right side of the dialog control
whether the option symbol currently displayed in the adjacent combo-box will be
plotted. They’re all enabled in this
example to facilitate comparing the rate sensitivity of the selected options to
that of the portfolio as a whole.
Portfolio
Positions must exist in the portfolio for the Portfolio
checkbox to be enabled. When enabled and
the checkbox is checked, an additional curve is plotted in black, representing
the cost weighted average of the rate sensitivity of all option positions in
the portfolio.
In the second example, the interest rate sensitivity of the
portfolio is relatively low. If your
interest is in getting a better view of the rate sensitivity of the portfolio,
you can disable some of the more rate sensitive options and the plot will
rescale to fill the vertical extent of the plot area. In the example below, VNLAX.X, INQSF.X, and
NQOC.X have been disabled. It’s now
apparent that the option portfolio will increase in value by 2% if the risk
free rate rises from its current 4.08% to 6%.
Risk Free Rate
The Risk Free Rate edit box displays the currently stored
value for the risk free rate. It’s
expressed as a percentage with a default value of 3%.
‘-‘ Edit Box
The ‘-‘ edit box specifies how far
below the current risk free rate to set the low X-value in the plot. This value cannot exceed the risk free rate.
‘+’ Edit Box
The ‘+’ edit box specifies how far above the current risk
free rate to set the high X-value in the plot.
The Time Decay Explorer provides a graphical view of
the relative rate with which option values decay as time passes. Options exhibit a variety of decay behaviors,
from near linear (WPJAB.X in green) and smooth decay (WNLAI.X in blue) to a
cliff-like drop (VLKML.X in purple) on the expiration date. The discontinuities in the green, purple, and
red curves occur at the respective underlying stock’s ex-dividend dates. ‘Today’ in the plot at right is December 14, 2007.
A call exercised before an ex-dividend date gives the
option holder the right to the dividend on the underlying stock. Waiting to exercise until after the
ex-divdend date leaves the right to the dividend with the current stockholder
of record, so the call loses value on that date. Applied Materials (AMAT) has an
ex-dividend date on August 14, so WPJAB.X, a Jan-2010 call on AMAT in green,
loses value on that date. Conversely,
put options gain value when an ex-dividend date passes. Kellogg (K) has an ex-dividend date on
November 15, so VLKMJ.X, a Jan-2009 put on Kellogg in red, gains value on that
date. Ditto for VLKML.X, a Jan-2009 put
on Kellog in purple.
The Time Decay Explorer uses the most accurate
approach available for computing Black-Scholes value and consequently is by far
the most computationnally intensive analysis in NillaHedge. That computational complexity derives from
the need to compute the present value of each potential dividend from the
present day to the specified End Date.
That may be as many as four dividends per year per issue in the
portfolio, at each point in time depicted on the plot (which may span multiple
years resulting in as many instances of each quarterly dividend).
The walk away consideration is that a multi-year plot
of a portfolio containing many options drawn upon stocks with multiple
dividends may post a wait cursor for much longer than you are accustomed to
elsewhere in NillaHedge. The good news
is that given the computational investment in the portfolio plot, its points
are only computed once when the dialog is posted (if the Portfolio button was
checked the last time you used it) or upon checking the portfolio box (if it
wasn’t checked the last time you used it).
Thus, subsequent changes in the selected (red, green, blue, and purple)
options will plot relatively quickly. As
your options portfolio grows, you will undoubtedly find it increasingly useful
to disable the portfolio plot before closing the dialog, so the next time that
the Time Decay Explorer posts, the decision to plot the portfolio will be
yours.
The Plot
Time-decay plots
depict time in months along the X‑axis and percent change in option value
along the Y‑axis.
The colors assigned
to option symbols are red, green, blue, and purple ordered from the topmost
symbol to the bottom (e.g. VLKMJ.X – red, WPJAB.X – green, etc.). When option positions exist in the database,
the Portfolio checkbox will be enabled, as it is here.
As you can see,
time-decay curves can be discontinuous, even exhibiting sharp vertical
drops. The compromise between accuracy
and responsiveness produces diagonal lines that would be perfectly vertical,
given infinite computing capacity. The
options and portfolio are not evaluated at every single visible point, but at
discrete intervals across the X‑axis.
One pixel of horizontal displacement is unavoidable, so a curve that
would appear as a nearly perfect vertical drop if all the points were plotted
will appear to have a very sharp slope instead.
Such approximations to the vertical impute no information whatsoever
about the value of the issue or portfolio at intervening X‑values; the Y‑values
at the rightmost point of the segment on top of the cliff and at the leftmost
point of the segment below the cliff are accurate, but in between nothing
whatsoever has been computed, the curve is merely an instrument of visual
continuity. You’ll note that more than
one pixel of deviation is evidenced in the plots on this page. At present, the the
selected options and the options portfolio (if it is enabled) are plotted at
sixty points in time, or about once every six days for a plot spanning one
year. On a QVGA (240x320 pixel) screen,
that’s one evaluation for every four horizontal pixels, resulting in three
unknown points between the ideally vertical segments.
Risk Free Rate
The Risk Free Rate
edit box displays the currently stored value for the risk free rate. It’s expressed as a percentage with a default
value of 3%.
End Date
The End Date picker
defaults to twelve months from the current date, but can be set earlier or
later to zoom the X-axis in or out, respectively. A ‘practical’ range of two months to four
years from the current date is enforced.
The EndDate of each these plots was extended
beyond the twelve month default to a bit over sixteen months, to capture
ex-dividend dates and the expiration of January 2009 options.
Plot Enabling Checkboxes
The checkboxes on
the right side of the dialog enable/disable plotting the time-decay of the
option symbol immediately at its left.
Portfolio
The Portfolio check
box enables you to see how your entire option portfolio responds to the passage
of time. The Time Decay Explorer plots a
polyline which sums all option positions in your
portfolio using each option’s cost-weighted contribution to the portfolio.
The plot at right
was drawn on 14-Dec-07.
VNLAC.X (purple) is a Jan-09 call on Intel, with Intel paying $0.45 to the
shareholder of record on November 3. VNLAE.X (red) is a Jan-09 put on Intel
Corp. (INTC).
VFOMA.X (blue) is a Jan-09 call on Ford Motor Co. (F), set up with Ford
paying a $0.20 on July 31. ANQDD.X is an
April-09 call Applied Materials (AMAT), with Applied Materials paying $0.24 to
the shareholder of record on August 14.
Obviously, it
doesn’t take a lot of positions in the portfolio for the ups and downs
associated with ex-dividend dates and option expiration dates to render various
discontinuities in the portfolio plot.
In this example, the portfolio consists of 100 of WPJMC.X, 100 of
VNLAE.X, 100 of VLKMJ.X, and 1100 of VFOMA.X.
Note that the rise in portfolio value associated with 1100 VFOMA.X put
options at Ford’s ex-dividend date (around 8 months from ‘today’) is subtler
than the expiration of 200 options (VNLAE.X and VLKMJ.X) in January 2009
(around 13 months from ‘today’). The
August 2008 (just over 11 months from ‘today’) ex-dividend rise due to 100 VLKMJ.X
puts on Kellogg is barely noticeable.
Pure Black-Scholes
mode
Y‑values on
the plot represent percentages of the option’s reference value, given by 
, where bsv represents the Black-Scholes
value at a given point in time and rv is a reference value which can be either the Black-Scholes value on the current date or the option’s currently
stored market price, based on the state of the Pure B-S checkbox. When Pure B-S is checked, rv is the
option’s reference value; when it’s unchecked, the stored market price is used for
rv.
The first
screenshot (previous page) shows a Pure B-S mode plot. You’ll note that all options start at time
zero with a 0% displacement from the reference value and ultimately finish at
-100% of the reference value.
In market price
mode (Pure B-S is unchecked) the ‘curves’ may start above or below 0% but
they’ll all finish at ‑100% since 
as 
. Options whose
currently stored market price exceeds the current Black-Scholes
value will start off showing a ‘loss’ (below 0%); options whose initial Black-Scholes value exceeds the currently stored market price
will start off with a ‘profit’ (above 0%).
Either way, the option or portfolio will decay in value from that
initial point. All options for a given
underlying stock are evaluated using the stock’s currently stored price,
volatility, and dividends. Since option
value increases with volatility, if the stored volatility is close to the
implied volatilities for the near-the-money options, the far-from-the-money
options will appear undervalued (therefore starting off with a ‘loss’ as
VPJMB.X does here) and vice-versa. If
the stock pays dividends and you have not entered any in the stock definition,
the market will undoubtedly have a different opinion about option value than
you will compute in their absence.
In the example at
right, note that the green (WFOMC.X) and purple (FMC.X) options actually increase in value over
time when viewed in market price mode (Pure-BS unchecked). This could be something to get excited about
because it means the current market price is below what an efficient market
would normally assess, i.e. there’s unrealized value within. However, in this case, the results were due
to accepting the default values for dividends (0.00) and volatility (0.3), when
in fact the defaults will frequently need refinement, i.e. garbage in will
invariably produce garbage out. If you
run into a situation like WFOMC.X or FMC.X after you’ve verified that the underlying
stock’s market price and dividends are correct and enabled in the Stock
Definition, and your opinion on volatility is right where you want it to be,
then a little excitement may be warranted.
Going Ex-Dividend
When ex-dividend
dates loom near, it’s possible that calls will begin to sell at a
discount. Likewise puts may begin to
incorporate a pro-forma ex-dividend premium.
There is currently no broadly accepted analytical model that accounts
for market premiums and discounts associated with nearby ex-dividend
dates. In all likelihood changes in
option value are somewhat less precipitous than an ideal present value
treatment (used here) would indicate.
Volatility Premiums
Options obviously
decay in value over time - some gradually, others abruptly. It therefore behooves you to be aware of how
your options portfolio behaves so you won’t be caught unaware when a
precipitous change in value is imminent.
Secondarily, switching between Pure B-S and market price mode can shed
light on disparities between theoretical and market value. In the plot above, VPJMB.X appears to have a
market price with a significant premium over its theoretical value. Similarly, VFOMU.X benefits from a large
premium in the plot at right. How can
market and theoretical values be so far off?
Of course, the market could be temporarily out of sync or the contract
writer might have unrealistic expectations, but (barring parameter error) more
often than not you are witnessing the effect of the volatility smile.
Options with
strikes distant from the current market price of the underlying stock (struck
far from the money) have implied volatilities greater than those struck close
to the market value. When you look at
implied volatility vs. strike price, you generally find a convex curve with its
low point near the stock’s market price.
The actual stock volatility is generally found at the low point. The portion of implied volatility beyond the
stock’s actual volatility is a reflection of increasingly bearish/bullish
investor expectations, i.e. very bullish/bearish option investors believe that
the stock’s volatility is inherently higher in order to rationalize their
market view. If you don’t share their
more dynamic view of the underlying stock’s volatility, you are bound to run
into option valuation disparities when analyzing options struck far from the
money.
The VPJMB.X case
will be discussed in more detail in the Volatility Value Explorer section on
Volatility Risk, so we’ll forego a detailed rationalization here. For now, it should be apparent that
significant departures from a conservative implied volatility (computed near
the current spot price on options with near term expiration dates) can have a
dramatic (non-linear) influence on
option value. Half of VPJMB.X’s implied volatility in the example above is premium
over a near term spot price assessment.
The Volatility Value Explorer finds that volatility premium on AMAT effects a 15x change in VPJMB.X’s
theoretical value.
The Volatility-Value Explorer provides a
graphical view of the relative sensitivity of options to their underlying
stock’s volatility. Up to four options
can be compared simultaneously. The
Volatility-Value Explorer has two modes of operation (really just ways to scale
the Y-values), pure Black-Scholes and market price
relative. In Pure Black-Scholes mode, the option’s current market price is ignored
- only the risk free rate and the underlying stock’s price and volatility
influence the plots. When the Pure B-S
check box is unchecked, the option’s last known market price becomes the
reference against which imputed option prices are scaled.
The Plot
The first thing to remember about volatility-value plots is
that both axes depict ratios, not
volatilities, option value, or percentages thereof. The horizontal axis depicts the ratio of
experimental volatility to the current volatility for the option’s underlying
stock, so 
represents the
currently stored volatility for the underlying stock. The vertical axis similarly depicts the ratio
of the imputed Black-Scholes value to the option’s
last known market price or its Black-Scholes value
(depending on the state of the Pure B-S checkbox), so 
represents the option’s
relative value at a given relative volatility.
The colors assigned to option symbols are
red, green, blue, and purple ordered from topmost symbol to bottom (e.g.
VPJMB.X – red, VPJAX.X – green, etc.). When
option positions exist in the database, the Portfolio checkbox will be
enabled. When checked, a black line
depicts the volatility-value curve for the current option portfolio with each
option’s contribution weighted by the cost of the associated positions (refer
to the screenshot below).
Plot Enabling Checkboxes
The checkboxes on the right side of the dialog
enable/disable plotting the volatility-value for the option symbol immediately
to its left. When options produce very
high value-volatility ratios while others are less responsive, it can be
difficult to assess the behavior of the low ratio options. In that case, you can disable (uncheck) the
high ratio options, triggering the plot to re-scale to accommodate the
remaining curves, thus providing more insight into the low ratio options’
behavior. Compare the first
Volatility-Value Explorer plot with the one at right.
Pure Black-Scholes mode
When Pure B-S is checked, the plot 
represents the imputed option value divided
by the Black-Scholes value at the reference
(underlying stock’s stored) volatility, consequently the volatility-value
curves all pass through 
. In market price mode
(Pure B-S is unchecked), the Y-values in the plot represent the imputed option
values divided by the option’s stored market price, so the volatility-value
curve can pass above or below 
.
All things being equal, a premium option, whose currently
stored market price exceeds its Black-Scholes value at
the currently stored volatility, will pass below as VPJMB.X (red) does
in the screenshot at right. Conversely,
a bargain option, whose Black-Scholes value at the
currently stored volatility is greater than the option’s currently stored
market price will pass above as VPJAE.X (purple)
does.
Portfolio
The Portfolio check box enables you to see how your entire
option portfolio is positioned with 
respect to volatility risk relative to the
currently stored volatility for the underlying stock. The Volatility-Value Explorer plots a curve
which sums all option positions in your portfolio, each option’s contribution
to the volatility-value curve being weighted by the cost of the position
relative to the total cost of the option positions in the portfolio. It’s unchecked at right to better show the
volatility-value curves for ANQAM.X and VPJAX.X.
Evaluation Date
The Evaluation Date picker defaults to the current date, but
can be set earlier or later to review how current parameters would affect
volatility-value in the past or future.
Risk Free Rate
The Risk Free Rate edit box displays the currently stored
value for the risk free rate. It’s
expressed as a percentage with a default value of 3%.
Volatility Risk
Volatility risk has been a key factor in the financial
difficulties at Barings Bank and at Long Term Capital Management, so it’s an
issue of very real concern to professional portfolio managers. Accurately hedging against volatility risk is
a complex topic beyond the scope of NillaHedge and
this documentation, but the Volatility-Value Explorer does help you to quantify
relative volatility risk, enabling you to make more informed choices.
The thing to remember about using the Volatility-Value
Explorer is that is depicts what happens to option prices as a function of
relatively heavy-handed modifications to the underlying stock’s
volatility. An assumption in analyses of
this sort is that the reference volatility is ‘reasonable,’ but it becomes a
critical assumption when attempting to assess relative volatility risk between
options not drawn on the same underlying stock.
The Volatility Smile
If you are not already familiar with the volatility smile,
it is a curve that results from plotting implied volatilities against strike
price, with implied volatility increasing as the strike distances itself from
the underlying stock price. In fact, the
smile is really a surface. If you
examine implied volatility versus time to maturity, you will note a similar
effect. Part of the reason for
non-constant implied volatility is that Black-Scholes
theory assumes that stock returns are lognormally
distributed, which means that the natural logarithm of stock returns is
normally distributed. The lognormal
assumption is attractive because it’s close to reality and analytically
tractable, but historical returns show that the actual distribution has
somewhat fatter tails and a higher peak at the mean.
So, volatility risk intuition is potentially clouded by the
volatility smile and our imperfect understanding of how to compare apples and
oranges, e.g. AMAT to INTC,
etc. Both potential problems are
ameliorated by scoping your comparisons to options in the same neighborhood
with respect to expiration and moneyness (degree to
which the underlying stock’s price is into the option’s profitable zone).
After using the Volatility-Value Explorer for a few minutes,
you’ll surely notice that low value, high implied volatility options are much
more likely to produce high option price ratios for a given multiple of
volatility than those with higher intrinsic value, as illustrated by VPJMB.X in
the previous four screenshots. VPJMB.X
is a Jan-07 Put with a $10 strike selling for $0.15 while its underlying stock
(AMAT) has a market value of $17.97.
It’s wise to review the volatilities assigned
to stocks underlying any options of interest before comparing the
volatility-value ratios of the associated options. Without venturing outside of the family of
options on Applied Materials (AMAT), note
that the second pair of plots in the Volatility-Value Explorer section used a
reference volatility of 0.231 (nearly VPJAE.X’s
implied volatility), causing VPJMB.X (red) to appear to be selling at a high
premium and producing vastly different volatility-value ratios in Pure B-S and
market price modes. In the next pair of
plots in this section, the reference volatility is the implied volatility for
VPJMB.X (
), so VPJMB.X now passes through in market price mode
and behaves identically in both modes.
Unfortunately, VPJAE.X (purple) now appears to be a bargain option,
demonstrating a similar Jekyl-Hyde schizophrenia when
switching between Pure B-S and market price modes because it feels mispriced. You may
also note that VPJAX.X (implied 
), which previously passed near now appears to be a
bargain option because the reference volatility is so much higher than its
implied volatility.
Alternatively, in the plot below right, we have four puts
all expiring in Oct05 with ANQVR.X (implied 
) struck out-of-the-money at $17, ANQVS.X (implied 
) struck slightly in-the-money at $18, ANQVT (implied 
) struck at $19, and ANQVD.X (implied 
) struck at $20, while AMAT
has a market value of $17.83. 
Certainly, we’ve come to expect that
out-of-the-money options exhibit higher volatility sensitivity, but since I
mentioned them, the question you might really want to ask is “What’s up with ANQVD.X’s implied volatility?” The first thing of note is its extremely low vega = 0.0011, while
its temporal brethren have vegas on the interval [1.78 .. 2.29), but perhaps more to
the point, its delta = -1.0 and
consequently its probability of closing in-the-money is 100%, meaning that
other factor sensitivities, including volatility, are not particularly
influential at the current stock price.
One conclusion you might draw from the foregoing discussion
is that you should always have a good understanding of what you’re looking at
in the Volatility-Value Explorer, but I hope the walk away benefit will be your
recognition of the degree to which volatility can drive option value, so you
won’t enter positions without assessing the risks and grappling with the model
parameters beforehand.
Compensating Volatilities
One technique that partially compensates for inaccuracies
introduced by the lognormal assumption is to use an Exponentially Weighted
Moving Average (EWMA) to compute the underlying stock trend and
volatility. J.P. Morgan’s RiskMetrics group produces well regarded Value-at-Risk
assessments using lognormal models in conjunction with EWMA volatilities. In Risk
Management, A Practical Guide,
Alan Laubsch recommends using decay factor 
. Using that decay
factor, 75 trading days (105 calendar days) capture 99% of an exponentially
weighted average, so the usual recommendation is to collect 80 trading days
(112 calendar days) of stock returns.
On-line sources leave something to be desired in this realm, but Carol
Alexander’s (2001) Market Models provides very accessible coverage of
volatility, exponentially weighted moving averages, and other models used in
portfolio management, without sacrificing any details. Given a set of daily returns, the volatility
at time t (
) is given by: 
, where 
are the daily
returns. Nobody has an infinite supply
of daily returns, but with , the influence of four month and older stock returns have
negligible influence on the value of the sum anyway. After establishing a starting point EWMA
estimate of the historical volatility, you can adopt a recursive model, e.g. 
. Such EWMA volatilities partially compensate for the
mismatch between actual stock returns and lognormal models, and the testimonial
is how extensively RiskMetrics’ approach is used by
banks to model their portfolio risk and compute reserve requirements. If you plan to use a volatility that differs
markedly from the RiskMetrics’ model discussed here,
you should know why.
Black-Scholes Greeks
& Elasticity
All of the variables used on the right hand sides below are
defined in the glossary entry for the Black-Scholes
value presented immediately after the greeks. The first derivative of the standardized
cumulative Normal distribution, expressed as 
, occurs frequently below - it’s defined in a Glossary entry
for the Normal distribution. In all
cases, the values reported for the Black-Scholes greeks in NillaHedge
are annual values. For simplicity’s
sake, all of the expressions for the greeks
below are based on a continuous dividend yield Black-Scholes
model. However, the Option Analyzer relies
primarily on a present value dividends model (not presented in the glossary
entries below) and only falls back to the continuous model in rare situations
where the present value model can’t be evaluated.
Delta measures the option’s sensitivity to the underlying
stock’s price. When the investment
objective is to hedge a stock position against risk, investors typically seek
to maintain what’s called a delta neutral position. That’s accomplished by selling 
shares of the underlying
stock for each option you own. Of
course, as the stock price changes, it will rapidly become apparent that this
is a moving target, hence the interest in gamma. See also:
Elasticity.
Calls: 
Puts: 
An option’s
elasticity is the option’s delta scaled into the relevant currency, i.e. 
, where V is the
option’s Black-Scholes value and S is the underlying
stock’s price. Elasticity indicates how
much movement you can expect in the option’s value given a change in the
underlying stock’s price, e.g. a call selling for $2.00 with 
on an underlying stock
selling for $30 has elasticity, 
, so a 1% increase in the stock price justifies a 6 %
increase in the market value of the call.
Puts generally have negative elasticity since changes in put values run
counter to movements in the price of the underlying stock.
Gamma measures the rate of change in delta with respect to
the underlying stock’s price. If you
want to maintain a delta neutral position in a given stock, an option with high
gamma will have to be re-hedged more often than one with low gamma, thus
potentially costing you more in transaction fees. Skilled hedge investors try to find two or
more options on the same underlying stock with counterbalancing gammas, thereby
constructing a (near) gamma neutral position which will thereby minimize the
need to re-hedge in response to movements in the stock price.
Puts & Calls: 
Rho(D)
Rho(D) is the option’s price sensitivity to changes in the
underlying stock’s dividends.
Calls: 
Puts: 
Rho(r)
Rho(r) is the option’s price sensitivity
to changes in the risk free rate.
Calls: 
Puts: 
Note:
Most systems don’t distinguish between rate sensitivities, reporting
only something vaguely called rho. NillaHedge’s 
is probably the
equivalent of other systems’ rho.
Theta
Theta measures the option’s price sensitivity with respect
to the passage of time (t).
Calls: 
Puts: 
John Hull and Paul Wilmott each give the expression above for theta, the first
derivative of option value with respect to time, and I concur. Please do not be misled by Henry
Tang’s derivation. Tang skips over a number of ‘trivial’ steps
in his derivation of theta for a vanilla call and loses track of the continuous
dividend yield discounting factor (
) in the first term.
If you decide to embark on a derivation of your own, you’ll quickly find
that the last two terms fall straight out of the product rule, but you may
initially scratch your head on how to convert (for a call) 
into the first
term. A detailed derivation is beyond
the scope of this documentation, but it should be obvious that 
is key
to the transformation. In particular,
you’ll need 
. Don’t bother
differentiating 
and 
; just knowing 
is enough. Good luck!
Vega measures the option’s price sensitivity to changes in
the underlying stock’s volatility.
Puts & Calls: 
Black-Scholes Value
There are a number of formulae that express the Black-Scholes value for an option. Many commonly assume that there are no
dividends, so the term 
, effectively making it disappear and simplifying the
expression for the Put and Call values.
The expression below is more accurate than tossing the dividends out the
window, but it’s not perfect because the continuous yield model accounts for
dividends on the underlying stock even in situations where the ex-dividend date
is after the option’s expiration date.
Real option prices respond to dividends whose ex-dividend date lands
between the present time and the option’s expiration date. NillaHedge uses the
present value of discrete dividends where possible rather than averaging the
dividend spikes through the calendar year as defined in the expressions below.
Early on, The Time Decay Explorer (TDX) always used the
continuous model, but the plotting architecture now allows it to apply the
present value model wherever it can be evaluated, hence the discontinuities in
TDX plots when dividends are defined in the underlying stock. Given the low likelihood that you’d ever come
across a discrete dividend version of Black-Scholes,
we’ve only presented the continuous yield version here. The following expressions are discussed in
several books authored by Paul Wilmott, as well as
one by John Hull, among others. Don’t be
put off by the N(x) expression below
- it’s just the standardized (zero mean with a standard deviation of one)
cumulative Normal distribution, discussed later in the Glossary.
|
|
C := call value
D := annualized dividend yield
K := strike price
P := put value
r
:= risk free rate
 := stock volatility
S := stock price
t
: = current date (years)
T := maturity date (years)
|
Assuming a standardized Normal distribution, the probability
of an event occurring at or below x
is given by:
The first derivative of the standardized cumulative Normal
distribution is the probability density function for a standardized Normal
distribution. The Normal
p.d.f. turns up frequently in expressions for various
Black-Scholes’ greeks as 
, defined as:
rate s
The probability of
closing In The Money is an indication of the
likelihood of that the option will expire with the stock price above the strike
if the option is a call; or below the strike price if the option is a put. This probability is a natural outgrowth of
Black-Scholes pricing theory, discussed below.
Calls: 
Puts: 
Volatility - a measure of the amount by which stock returns
have fluctuated (historical volatility) or are expected to fluctuate (expected
volatility) in the future. The
volatility of a stock is the standard deviation of the continuously compounded
rates of return over a specified period.
It’s equivalent to the standard deviation of the differences in the
natural logarithms of the stock prices plus dividends, if any, over the
period. Although the observation period
may be less than a year or several years, by convention, volatility represents
the standard deviation in the stock’s annual returns. The higher the volatility, the more you can
expect returns on the stock to vary.
Volatility is sometimes quoted as a percentage, but in NillaHedge, it’s not scaled up by 100. If you use volatility from a source that
reports it as an annual percentage, be sure to scale it back down. An excellent source for volatility values
(reported as percentages) is Robert's Historical Stock
Volatilities. An excerpt appears in the Resources section,
near the end of the user manual.
Robert's
Historical Stock Volatilities – Robert’s will produce a report that looks
something like the following table for Intel Corp.
|
Ticker
|
1 Month
|
2 Month
|
3 Month
|
6 Month
|
9 Month
|
1 Year
|
2 Year
|
3 Year
|
4 Year
|
5 Year
|
|
INTC
|
32.03%
|
27.95%
|
28.32%
|
33.74%
|
30.90%
|
30.67%
|
34.13%
|
46.46%
|
51.06%
|
62.57%
|
Obviously, there are many possible answers for a given
stock’s volatility, depending on your observation window. The situation is complicated by the fact that
options typically incorporate investor’s beliefs about the underlying stock’s
expected volatility. If you believe that
a stock’s returns will be less volatile than they have been historically, then
the value of options on that underlying stock will be consequently less
valuable. You can get a sense for what
other investors believe the stock’s expected volatility will be by looking at
the volatility implied by current option prices on that stock. Even there, beware that implied volatility is
generally not constant across all strike prices and expiration dates - you must
still use your own judgment to interpret the implied volatilities observed.
[Hull]
Options, Futures, and Other Derivatives, Fifth Edition
John C. Hull. 2002 Prentice Hall
This is an excellent reference on
everything from interest rate markets, credit risk, hedging strategies, Black-Scholes theory, the greeks,
volatility smiles, etc. Hull
continues on into exotic options, interest rate derivatives, swaps,
Value-at-Risk, using moving averages to compute volatilities, and more. Very little of Hull’s
book could be edited out without losing something valuable and Hull’s
section on spreads is much more useful than Wilmott’s.
[Wilmott] Paul Wilmott Introduces Quantitative Finance
Paul Wilmott. 2001 John Wiley & Sons,
Ltd.
Wilmott
has written various books in the computational finance arena, one being a
two-volume set (a greatly expanded version of this text), but in this
particular text Wilmott and Hull
seem to be competing head-on. While Hull
and Wilmott each spend a chapter on binomial models,
Monte-Carlo methods, value at risk, and credit risk, Wilmott
extends that treatment with chapters on portfolio management, RiskMetrics, and CrashMetrics, though
these issues are probably beyond the call for the typical NillaHedge
user. Wilmott
has probably over-diagramed this book - on a content per page basis, I’d pick Hull’s
book unless you need or want the chapters on portfolio theory, RiskMetrics, and CrashMetrics.
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