Copyright © 2007 by Mike
Landis
Published
by PocketNumerix, Inc.
All rights reserved.
Reproduction or translation
of any part of this work beyond that permitted by Section 107 or 108 of the
1976 United States Copyright Act without the permission of the copyright owner
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Requests for permission or
further information should be addressed to:
Mike Landis
PocketNumerix, Inc.
Table of
Contents
Strategies
Supported. 4
Strategy. 4
Option
Expiration. 5
Ratio
Spreads. 5
Non-negative
Values. 5
Quantity
Zero. 5
Graph
Colors. 5
Database
Access. 5
Restoring
the previous state. 5
Option
Only Strategies - Bullish. 6
Synthetic
Long Stock. 6
Bull
Call Spread. 6
Bull
Put Spread. 6
Option
Only Strategies - Bearish. 7
Synthetic
Short Stock. 7
Bear
Call Spread. 7
Bear
Put Spread. 7
Option
Spreads - Neutral, Low Volatility. 8
Strangles. 8
Butterfly
Spreads. 8
Option
Only Strategies - Neutral, High Volatility. 9
Long
Straddle. 9
Strangles. 9
Strategies
Involving Stock - Covered. 10
Strategies
Involving Stock - Protective. 11
Protective
Put 11
Protective
Call 11
Strategies
Involving Stock - Bracketed. 12
Collar 12
Fence. 12
Strategies
Involving Stock - Arbitrage. 13
Conversion. 13
Reversal 13
References. 14
The StrategyExplorer
is a graphing tool allowing you to experiment with various hedging strategies
optionally including a stock and as many as three options on that stock. It assumes that all options on the stock
expire on the same calendar date. It
displays an auto-zoomed window on a region of the underlying stock’s price with
the vertical axis representing gains (losses) imputed by stock prices.
The StrategyExplorer helps you
analyze option spreads, enabling you to hedge risk or maximize profit
potential. You can think of the StrategyExplorer as a hedge-specific graphing calculator
with built-in examples of twenty popular option spreads.
You’ll notice that the StrategyExplorer
plots payoff polylines for each of the constituent
options as well as the aggregate profit (loss) on the spread, but it doesn’t
bother plotting the Black-Scholes values for the
options or the sum of those values.
There are two reasons for this.
First, it would require capturing the option’s times to expiry, for
which little room remains on the tiny PocketPC
screen. Second, computing enough option
values to produce a smooth plot would slow the application down, perhaps
unacceptably. Option arbitrage
specialists won’t be happy about this – they’ll have to wait for a future
release when beefier PocketPC processors are
available.
Strategies Supported
Trivial strategies involving a single option or a single
stock are not explicitly discussed below, but are clearly constituent
components in the strategies presented.
The StrategyExplorer really becomes useful in
analyzing the profit profile of a stock and/or a combination of options
expiring concurrently on that underlying issue.
Each of the positions may be either long or short. Twenty commonly used strategies have built-in
examples, so you can start with the example and modify prices to meet your
situation. We’ll cover the strategies
themselves in the order that they appear in the Strategy combo-box. The strategies are not listed alphabetically, they are grouped into those involving only
options and those involving both options and stock, with the options only
strategies appearing first. The options
only strategies further break down into the following subgroups: bullish, bearish, neutral with low volatility,
neutral with high volatility. Strategies involving stock break down into
the following small subgroups: covered,
protective, bracketed, and arbitrage.
You don’t actually need the Strategy combo-box to run the StrategyExplorer, but you’ll probably find it
convenient. The Strategy combo-box
contains a list of twenty popular option spreads and hedging strategies. If you’ve never used it before you can use
arrow keys or the drop-down box to navigate the list of strategy names. If you know some of the strategy names, you
can type a couple of characters and have auto-completion find the strategy name
for you.
If you have never used the StrategyExplorer
before, the Strategy combo-box selects Synthetic Long Stock (the first strategy
in its list of strategies) as the strategy to evaluate, but if you’ve used the StrategyExplorer before, the Strategy combo-box will
display ‘Previous Settings’ and those settings will drive the plot.
Option Expiration
All of the spreads supported by the StrategyExplorer
are classified as vertical spreads. That means that all options are
assumed to expire on the same day, at some point in the future, i.e. they
haven’t expired.
Ratio Spreads
Every strategy supported is inherently a ratio spread.
Although the strategies that appear in the Strategy combo-box are usually
thought of as having integral values for the stock and option quantities, the StrategyExplorer is not limited to analyzing the accepted
discrete definition of a spread.
Non-negative Values
Each of the edit boxes accepts a non-negative value.
Negative values will be complemented and echoed back. Short sales are accomplished by selecting a
Sell radio button instead of a Buy button.
Quantity Zero
The quantity zero prevents a stock or option from being plotted
or contributing to the aggregate payoff.
Graph Colors
The output graph always displays the payoff polyline for the first option in red, the second option in
green, the third option in blue, and the stock in purple. It also plots a black polyline
over the constituent positions to represent the aggregate payoff.
Database Access
The StrategyExplorer does not
access the database, so the skeleton options you define and quantities you buy
or sell can be completely unrelated to actual options defined or positions you
hold. The StrategyExplorer
is intended to be an exploratory tool, unconstrained by the realities of the
markets or your portfolio.
Restoring the Previous State
The StrategyExplorer remembers the
state of your last analysis, so you can exit out of it at any time to define an
option, create a position, etc. and come back to exactly the point you were
when you left. The dialog’s saved state
is only accessed at initialization – once you’ve made changes to the state of
its controls, you can’t return to the ‘last saved state’.
A Synthetic Short Stock is a bearish strategy whose profit
(loss) behavior is identical to that of a short position in the underlying
stock with the advantage of requiring substantially less capital. Ideally, it’s constructed from a short
at-the-money call (red) and a long at-the-money put (green).
A Bear Call Spread is a bearish strategy constructed from a
short in-the-money call (red) and a long out-of-the-money call (green). It achieves exactly the same result as a Bear
Put Spread with a profit profile similar to a short position in the underlying,
except that both profits and losses are capped.
A Bear Put Spread is a bearish strategy constructed from a
short out-of-the-money put (red) and a long in-the-money put (green). It achieves exactly the same result as a Bear
Call Spread with a profit profile similar to a short position in the
underlying, except that both profits and losses are capped.
Short Straddle
A Short Straddle is a neutral
strategy, betting on little or no movement in the underlying stock price.
Ideally, it’s constructed from a short at-the-money call and a short at-the-money
put with the same strike. It has limited profit potential, but can
produce unlimited losses, as shown in the example at right.
Strangles broaden the low volatility region of straddles by separating
the strikes.
Short
Strangle
Short Strangles
exhibit limited, fairly likely profits, but potentially unlimited losses as
depicted in the example immediately below.
Short Strangles exhibit likely finite profits, but
potentially unlimited low probability losses.
A Butterfly Spread is a neutral
strategy with an upside like a Short Straddle, but limited losses. It can be constructed from calls or puts,
including two short options struck at-the-money and two long options with
strikes bracketing the spot price. The
profit zone can be extended by selecting bracketing options further from the
spot price, at somewhat higher cost.
A Long Straddle is a neutral strategy, betting on a big move
in the underlying stock price, so it’s a high volatility play. Ideally, it’s constructed from a long
at-the-money call (red) and a long put with the same strike (green). Peak losses occur at the strike, with gains
on both sides of the strike if the underlying moves sufficiently far away from
the strike. It exhibits limited likely
losses, but potentially unlimited profits.
Strangles are similar to Straddles
except that the strikes on the options are pulled away from the spot price of
the underlying.
Long Strangle
Both options are struck out-of-the-money, so Long Strangles are generally less expensive strategies to pursue than Long
Straddles. Long Strangles exhibit limited,
fairly likely losses, but potentially unlimited profit potential, as shown in
the example at left.
Covered Call
A Covered Call strategy, also known as a Synthetic Short
Put, is a strategy wherein the writer (seller) of the call owns the underlying
stock on which the option is written.
Covered calls are generally written in situations where the writer
already owns the underlying and believes that the market has implied too much
volatility in the underlying stock.
Since option prices rise with volatility, if the market is
implying too much volatility, it’s possible to capture the premium represented
by the difference in option prices resulting from the difference between the
perceived and implied volatilities.
Naturally, the seller hopes that time decay will render the short call
worthless at expiry, turning the entire premium received into profit. Refer to the example at right.
Covered Put
A Covered Put strategy, also
known as a Synthetic Short Call, is a strategy involving selling stock and a
put against that underlying, though some traders simply sell the put and hold
cash to cover the downside. Selling a
put by itself is bullish. Coupled with a
short stock, the upside here is capped and the downside is potentially
unlimited.
Covered puts can be used to target a buy price on the
underlying. The writer would set the
option’s strike at the target price. The
premium received effectively reduces the current stock price. Put writers like to issue options when they
believe a rapidly falling (high volatility) stock has bottomed out. Refer to the example at left.
A Protective Put strategy, also known as a Synthetic Long
Call, is a bullish strategy constructed from a long stock (purple) and a long
put (red). This strategy hedges the
downside in the stock position while retaining the upside profit potential.
A Protective Call strategy, also known as a Synthetic Long
Put, is a bearish strategy constructed from a short stock (purple) and a long
call (red). This strategy hedges the
upside in the stock position while retaining downside profit potential.
Collar
A
Collar has the same profit profile as a Bull Spread, but unlike a Bull Spread
(which doesn’t include a position in the underlying stock), the Collar is
typically used to protect profits in a pre-existing long stock position
(purple) by bracketing the long stock position with a long out-of-the-money put
(red) and a short out-of-the-money call (green).
It
may also be constructed by hedging the downside of a Covered Call with a long
out-of-the-money put.
While
losses are limited, further profits are similarly capped.
A Fence is a bearish strategy with the same profit profile
as a Bear Spread. Unlike a Bear Spread, which
is constructed from two options, the Fence includes a position in the
underlying stock. A Fence is typically
applied to protect profits already accrued in a short position in the
underlying stock. It is constructed from
a short stock, a short out-of-the-money put, and a long out-of-the-money call,
as shown in the chart at left.
If C is the call price, P
is the put price, S is the stock price, and K is the strike price, and Put-Call
Parity is not true, there may be an opportunity for a risk-free profit through
arbitrage. Put-Call Parity is often
cited as 
or sometimes as 
where the strike in the simplistic model is replaced by its
present value, but a more accurate picture also deducts the present value of
dividends through expiry, thus 
. Obviously, this
model only applies to situations where the put and the call share the same
strike and expiration date.
You can use the StrategyExplorer
to evaluate potential arbitrage opportunities by setting the price of the
underlying stock and two of its options (a put and a call) with the same
strike, bearing in mind that StrategyExplorer does
not account for the time value of money.
To get an accurate portrayal of arbitrage profit potential, you need to
discount the stock price by the present value of the strike and the present
value of any outstanding ex-dividends.
If there’s any displacement above or below the horizontal axis, you can
capture a risk-free profit on the spread if transaction fees are less than
remaining margin.
Conversions are used by floor traders to capitalize on
discrepancies between the pricing of calls and puts. When calls are overpriced relative to puts
(the premium is grossly exaggerated in the example at right), a short term, riskless profit is available using a Conversion. A Conversion is constructed from a Synthetic
Short Stock (a short call and a long put at the same strike), exactly offset by
a long position in the underlying stock.
If the profit line falls below the X-axis,
you can execute a Reversal instead.
Reversals are Reverse Conversions. They are used by floor traders to capitalize on
discrepancies between the pricing of calls and puts (the premium is grossly
exaggerated in the example at left).
When puts are overpriced relative to calls, a short term, riskless profit is available via a reversal. A reversal is constructed from a Synthetic
Long Stock (a short put and a long call at the same strike), exactly offset by
a short position in the underlying stock.
If the profit line falls below the X-axis, you can execute a Conversion
instead.
References
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.
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 I needed the chapters on portfolio theory, RiskMetrics,
and CrashMetrics.
