Transcript Common Option Strategies - NYU Stern School of Business

Deutsche Bank
Common Option Strategies
Alan L. Tucker, Ph.D.
631-331-8024 (tel)
631-331-8044 (fax)
[email protected]
Copyright © 1997-2001
Marshall, Tucker & Associates,LLC
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Deutsche Bank: Common Option Strategies
Copyright (c) 1997-2002 Marshall, Tucker &
Associates, LLC
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ALAN L. TUCKER, Ph.D.
Alan L. Tucker is Associate Professor of Finance at the Lubin School of Business, Pace University, New York, NY and an Adjunct
Professor at the Stern School of Business of New York University, where he teaches graduate courses in derivative instruments. Dr.
Tucker is also a principal of Marshall, Tucker & Associates, LLC, a financial engineering and derivatives consulting firm with
offices in New York, Chicago, Boston, San Francisco and Philadelphia. Dr. Tucker was the founding editor of the Journal of
Financial Engineering, published by the International Association of Financial Engineers (IAFE). He presently serves on the
editorial board of Journal of Derivatives and the Global Finance Journal and is a former associate editor of the Journal of
Economics and Business. He is a former director of the Southern Finance Association and a former program co-director of the 1996
and 1997 Conferences on Computational Intelligence in Financial Engineering, co-sponsored by the IAFE and the Neural Networks
Council of the IEEE.
Dr. Tucker is the author of three books on financial products and markets: Financial Futures, Options & Swaps, International
Financial Markets, and Contemporary Portfolio Theory and Risk Management (all published by West Publishing, a unit of
International Thompson). He has also published more than fifty articles in academic journals and practitioner-oriented periodicals
including the Journal of Finance, the Journal of Financial and Quantitative Analysis, the Review of Economics and Statistics, the
Journal of Banking and Finance, and many others.
Dr. Tucker has contributed to the development of the theory of derivative products including futures, options and swaps, and to the
theory of international capital markets and trade. He has also contributed to the theory of technology adoption over the life-cycle.
The Social Sciences Citation Index shows that his research has been cited in refereed journals on over one hundred occasions.
As a consultant, Dr. Tucker has worked for The United States Treasury Department, the United States Justice Department, Morgan
Stanley Dean Witter, Union Bank of Switzerland, LG Securities (Korea), and Chase Manhattan Bank. Dr. Tucker holds the B.A. in
economics from LaSalle University (1982), and the MBA (1984) and Ph.D. (1986) in finance from Florida State University. He was
born in Philadelphia in 1960, is married (Wendy) and has three children (Emily, 1993, Michael and Matthew, both 1995).
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Common Option Strategies
Purpose. The purpose of this presentation is to illustrate common option
trading strategies. Our focus will be on three types of strategies:
(1) Those that capture potential profits arising from how
realized/future volatility comports with a trader’s “view” on volatility.
(2) Strategies that capture arbitrage profits arising from differences in
the values of embedded options and their actual or synthetic
counterparts.
(3) Collar trades and related trades designed for the particular needs of
certain high net worth retail clients.
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Common Option Strategies
• Keep in mind the following throughout our discussion:
– Strategies (1) and (2) are appropriate for institutional traders
whereas (3) is appropriate for retail clients.
– With (1), a trader (e.g., a “volatility directional hedge fund”
or the “prop desk”) is taking a position in vol and thus
profitability depends critically on whether or not his “view”
proves correct. Limits on an options dealer, e.g., a limit on
the vega of a dealer’s book, prevent excessive losses and
therefore limit gains from these types of strategies.
– The arbitrage strategies (2) are also generally the purview of
hedge funds and other “buy side” entities.
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Common Option Strategies
Example 1. Assume that for a particular stock, a trader believes that the
stock’s implied volatility term structure is too low, as illustrated below.
(Potential reasons motivating this and other views will be discussed
shortly. Note that the example could just as readily be imparted in
terms of forward implied volatility term structures.) How can a trader
“monetize” the move from implied to predicted volatility?
Volatility
Predicted Vol
Implied Vol
Option Maturity
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Common Option Strategies
In this example, the trader wants to be “long vol” to profit from
a rise in option premium occasioned by an upward shift in the
implied volatility term structure toward that predicted. To be
“long vol” while simultaneously immunizing against changes in
the stock price, the trader wants to assume a position that is
delta and gamma neutral but exhibits a positive vega.
For instance, suppose that the trader wants a delta and a gamma
of 0 and a vega of say +210,000. In order to change N
greeks/risk metrics, one has to trade at least N+1 assets. Let
there be two actively traded options on the stock (with maturity
equal to or extending beyond the relevant segment of the
implied volatility term structure) having the following greeks:
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Common Option Strategies
Option 1
Option 2
Delta
0.50
0.60
Gamma Vega
0.030 1.80
0.015 1.60
Here the trader must solve the following small system of
equations:
(1) w1(.03) + w2(.015) = 0
(gamma equation)
(2) w1(1.8) + w2(1.6) = 210,000
(vega equation)
The solutions are w1 = -150,000 and w2 = 300,000. Assuming
100 shares per option contract, the trader must write 1500
contracts of Option 1 and buy 3000 contracts of Option 2.
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Common Option Strategies
At this point, the trader has a delta of: (-150,000)(.50) +
300,000(.60) = 105,000. Therefore, the trader must sell off
from inventory or short 105,000 shares in order to delta hedge.
The new book vega of 210,000 suggests that the trader will
have an instantaneous profit of about $2,100 should the implied
volatility term structure shift up (in a parallel fashion) by 0.01.
Why “instantaneous”? (Dynamic trading to hit bogies.)
Why “about $2,100”? (Option prices are non-linear in vol.)
How many asset were traded? (N+1 rule.)
Is the new vega within limits? (Risk tolerance.)
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Common Option Strategies
What would happen if the implied volatility term structure was
perceived as too high? Then the trader would want to be “short
vol”. That is, the trader would want to be delta and gamma
neutral and simultaneously carry a targeted vega that was
negative.
In general, is it more dangerous to be long vol or short vol?
The answer is short vol because volatility can go up without
bound whereas it can only go down to zero. Like stock prices,
volatility is reasonably described by a log-normal distribution.
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Common Option Strategies
For equities in general, which strategy has made money recently, being
long vol or being short vol? The answer is short vol, at least since the
beginning of the 2001 calendar year. Option time values were “taken
in” during 2001 arguably because there has been a “volatility supply
glut” or “volatility overhang”. If one thinks of volatility as a
commodity like wheat, then it is feasible that the “price of equity
volatility” (option time values) can fall if there is a volatility overhang.
Excessive volatility supply can lower option time value and therefore
implied volatility, thus making a short vol strategy profitable. This
recent vol overhang in the equity market (a “vol crush”) appears to be
driven by the growth in the convertible bond issuance marketplace.
For most of 2001, convertibles made up about 55% of the total equity
issuance marketplace. This compares with a figure of just 17% in
1999. Convertibles of course have embedded equity options, and thus
the increased supply of vol.
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Common Option Strategies
The reason for this increase in convertibles appears to be two-fold: (1) certain
perceived tax and accounting advantages to convertibles (e.g., an issuer avoids
having to report more fully-diluted EPS under a convertible than under a
straight-equity follow-on issue). And (2), a recent propensity for investmentgrade firms to issue convertibles, whereas the convertible marketplace has
traditionally been composed of non-investment grade issuers (78% in 1999 but
only about 37% in 2001) seeking to lower their coupon rates. This may be due
to these firms no longer viewing their equity as “cheap currency”.
On the other hand, being long vol tended to be the winning strategy throughout
most of the second half of the 1990s as the Asian crisis, LTCM crisis, and other
crises tended to inflate volatility. For instance, the implied vol of the 6-month
S&P500 rose from about 12% in January of 1995 to about 22% in December
1999, and hit a high of about 35% in the first quarter of 1999. Being long vol
has also been profitable since the events of 11 September 2001.
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Common Option Strategies
The preceding discussion of convertibles and volatility
overhang suggests another recently popular trading strategy
undertaken by so-called “relative value volatility funds”. Here
the funds short options written on companies that have issued
convertibles (either by purchasing the individual convertible
bonds and financing the purchases via the repo market, or
writing options on a basket of the common stocks of the issuing
companies), and simultaneously long options written on a
basket of non-convertible common stocks. The idea of course
is to wager on a relative volatility compression between the two
types of companies - convertible bond issuing and non-issuing.
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Common Option Strategies
Example 2. Suppose that a trader feels that a stock’s implied
volatility, at a particular point or segment on its implied vol
term structure, is temporarily high and will revert toward the
general level of the rest of the term structure. How can the
trader capture value here?
Here the trader will want to be short vol with respect to this
particular point/segment on the term structure, but will want to
be vega neutral for the other segments of the term structure.
The easiest solution is to trade a forward-starting option whose
value would be principally driven by the relevant forward
implied vol.
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Common Option Strategies
Suppose the term structure looks as follows:
Implied Volatility
0
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0.25
0.50
0.75
1.00 Option Maturity (Years)
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Common Option Strategies
Writing the 9-month option and buying the counterpart 6-month
option would have the effect of carving out a short position in a
3-month option whose maturity begins in 6 months. An OTC
trade would simply be a short position in a straight forwardstarting option. Either way, the trader’s vega exposure is
isolated to the relevant segment of the implied volatility term
structure. So the trader would have a negative vega with
respect to the 3-month forward vol six months hence. Note,
however, that while the trader can delta hedge in the usual
fashion there will remain some gamma risk exposure from this
strategy.
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Common Option Strategies
Example 3. Suppose that a trader feels that an implied volatility term
structure will “twist”, for example, short-end vol will rise while longend vol will contemporaneously fall as illustrated below, perhaps
because of anticipated vol overhang in the longer run.
Implied Vol Term Structure
Existing
Predicted
Option Maturity
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Common Option Strategies
Of course, one way of trading on this anticipated twist is to
long short-end vol and short long-end vol. In other words, the
trader wants to carry a positive vega against the short-term
bucket of the term structure, and carry a negative vega against
the long-term bucket. Here both delta and gamma hedging can
be accomplished.
For example, suppose there exists the following two call
options:
Delta Gamma Vega Maturity Implied Vol
Option 1
0.65
0.04
2.60 0.75
40%
Option 2
0.50
0.02
1.80 0.25
30%
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Common Option Strategies
If the trader wants an exposure to the long vol of about -25,000 vega
and an exposure to the short vol of about +30,000 vega, then he could
write 100 contracts of Option 1 and buy 200 contracts of Option 2.
The short vol vega would be (-100)(100)(2.6) = -26,000 and the long
vol vega would be (200)(100)(1.8) = 32,000. The gamma position
would then be zero: (-100)(100)(.04) + (200)(100)(.02) = 0. The delta
position would be 3,500: (-100)(100)(.65) + (200)(100)(.50) = 3,500.
The trader could short 3,500 shares of the stock to delta hedge.
Thus the trader would have zero delta and gamma and nearly the vegas
desired. Obviously, the term structure would have to twist in the
direction predicted, and do so before the expiration of the shortermaturity option, to occasion profits. Also, the positions would need to
be re-balanced over time.
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Common Option Strategies
Example 4. Suppose that a trader computes two types of volatility
term structures - an implied vol term structure based on current
option market data, and a historic vol term structure based on a
GARCH(1,1) model. (See “Understanding Volatility”.) The
historic term structure is both downward sloping and
everywhere below that of the implied term structure. Because a
GARCH model accommodates mean reversion in the term
structure, this scenario would suggest two things: first, implied
vols may be too high in general and, second, volatility will
temper as it is rolled-out in time. To capture profits from the
latter, a trader would write short-term options, buy them back as
they unwind, and repeat this process through time.
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Common Option Strategies
Example 5. Suppose that an option dealer convinces his desk manager as
well as the middle office that current implied vol is historically high
and that implied vol is mean reverting (see J. Stein, J. of Finance,
1989). This dealer would want to write options at prices reflecting the
current and high implied vol, but base his hedging strategies on the
lower, long-run vol to which the implied vol will presumable revert.
For example, suppose the implied vol for a stock option is 70% while
the historic average is , say, 40%. The dealer writes one contract, with
a delta - based on the 70% vol - of 0.60. The delta would thus be
(-100)(.60) = -60, implying the need to purchase 60 shares to delta
hedge. But here the dealer conducts his delta hedging based on the
historic vol of 40%, which occasions a delta of, say, just 0.50. So the
dealer only purchases 50 shares of stock. This will lower the financing
costs of delta hedging. If the implied vol reverts to the historic
average, then the purchase of 50 shares will have proved an adequate
hedge, ceteris paribus.
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Common Option Strategies
Example 6. Traditional volatility wagers for retail traders
included straddles and their variants (straps and strips),
butterfly spreads, calendar spreads, and the like. Volatility
wagers for more sophisticated buy-side clientele include:
-Range Accrual Notes. Here the investor is paid a fixed amount
for every day a specified stock or stock index remains within a
fixed range. Buyers make profits when vol is low and writers
make profits when vol is high.
-Range Options. Here the investor has a payoff that is a
function of the realized range of the underlying stock value.
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Common Option Strategies
Consider the following range option payoff:
MAX{0, [(S(0) x k1)/(R + k2) - X]},
where R represents the realized range of the underlying asset. Here
the call buyer would be short vol, implying that this option has a
negative vega. For instance, let S(0) = X = $25, k1 = 6, and k2 = 0.
At inception, this option would have infinite intrinsic value as R is
zero. Thus the option value can only go down as the option unwinds
(a positive theta). As the stock price changes and the range, R, grows,
eventually the option will be knocked out (a dual-barrier option with a
stochastic knockout price). Why? By letting k2 be positive, the call
writer has limited liability. Why? The option’s value (and therefore its
greeks) is also influenced by where the current stock price is relative
to the already realized range. Why?
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Common Option Strategies
Example 7. Now let us turn our attention to pure vol arbitrage. Perhaps
one of the earliest examples of vol arbitrage involved callable bonds.
During the second half of the 1980’s, interest rate derivative desks
discovered that the call option embedded in a callable bond could be
replicated by a swaption. As a result, underwriters, working with their
interest rate derivatives desks, schooled corporate treasury officers on
how to issue a callable bond and then sell-off (economically speaking)
the embedded call by writing a swaption. If the embedded call could
be purchased cheaply by the corporate issuer, that is, the added coupon
was small compared to the straight-bond alternative, then the
corporation’s overall funding cost would be lower (than the straightdebt alternative) after selling off the call by writing the swaption. At
the end of the day, the embedded call was cheaper if its implied vol
was lower than that of the swaption. We have:
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Common Option Strategies
Issue callable bond
+ Write a swaption
Issue straight debt
(Issue straight bond and buy back a call)
(Sell off the embedded call)
(Lower coupon than issuing straight debt
directly if the implied vol of the swaption
is greater than that of the embedded call)
Of course, the investment bank could help discover value for the buyside under this same process. If the implied vol of the embedded call
is greater than that of the swaption, then the investor could buy the
bond (possibly financing the purchase in the repo market) and buy the
swaption. To isolate the value more precisely, the buyer could hedge
the credit risk of the bond with a credit derivative.
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Common Option Strategies
This process is essentially repeated now in the convertible
bond arbitrage game. The following attachment demonstrates
how an investor can engage in volatility arbitrage related to
differences in implied vol between the embedded option in the
convertible and an actual or synthetic option on the stock. (See
attachment titled “Convertible Bond Arbitrage”.)
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Common Option Strategies
• Example 8. Zero-cost collars and their variants are popular
strategies applicable to certain high net-worth retail clients.
(Currently there are about 60,000 U.S. citizens whose net worth
is $30 million or more.) The attachments titled “Constructive
Sales and Contingent Payment Puts” and accompanying
“Proof” provide detail.
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Common Option Strategies
Convertible Bond Arbitrage
A convertible bond may be viewed as a portfolio consisting of a long position in a
straight bond of the issuer and a long position in a call option on the issuer’s stock. The
bond component may be viewed as itself having two components: A pure interest rate
component and a credit component. That is:
Convertible Bond
Bond
Component
(long)
long
Call Option
Component
(long)
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Deutsche Bank: Common Option Strategies
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Interest Rate
Component
(long)
Credit
Component
(long)
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Common Option Strategies
Bond
Component
(long)
Convertible Bond
long
Call Option
Component
(long)
Interest Rate
Component
(long)
Credit
Component
(long)
Suppose that a convertible bond on XYZ is trading at a price that makes the embedded
call option look cheap. That is, if you value the converts’ components, the call is trading
at a low “vol.” Suppose the embedded call is trading at a vol of 20 when pure call
options on this stock are trading at a vol of 50. What would you do?
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Common Option Strategies
ARB
Buy Convertible Bond
Convertible
Bond
repo rate
LIBOR + X bps
Repo Market
Finance the position in
the repo market
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Common Option Strategies
Interest Rate Swap to strip away
interest rate component
LIBOR
ARB
Deutsche Bank
Fixed
Buy Convertible Bond
Convertible
Bond
repo rate
LIBOR + X bps
Repo Market
Finance the position in
the repo market
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Common Option Strategies
Default Swap to strip
away credit component
Interest Rate Swap to strip away
interest rate component
Fixed
LIBOR
ARB
Deutsche Bank
Deutsche Bank
Fixed
conditional
payment
Buy Convertible Bond
Convertible
Bond
repo rate
LIBOR + X bps
Repo Market
Finance the position in
the repo market
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Common Option Strategies
Option Market
or
Equity Market
Sell Call
or
Delta Hedge
Default Swap to strip
away credit component
Fixed
Interest Rate Swap to strip away
interest rate component
LIBOR
ARB
Deutsche Bank
Deutsche Bank
Fixed
conditional
payment
Buy Convertible Bond
Convertible
Bond
repo rate
LIBOR + X bps
Repo Market
Finance the position in
the repo market
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