Chance/Brooks An Introduction to Derivatives and Risk Management, 9th ed. Ch. 7: 1
Chapter 7: Advanced Option Strategies
Read every book by traders to study where they lost money. Read every book by traders to study where they lost money. You will learn nothing relevant from their profits (the You will learn nothing relevant from their profits (the markets adjust). You will learn from their losses.markets adjust). You will learn from their losses.
Nassim TalebNassim Taleb
Derivatives StrategyDerivatives Strategy, April, 1997, p. 25 , April, 1997, p. 25
Chance/Brooks An Introduction to Derivatives and Risk Management, 9th ed. Ch. 7: 2
Important Concepts in Chapter 7
Profit equations and graphs for option spread strategies, Profit equations and graphs for option spread strategies, including money spreads, collars, calendar spreads and including money spreads, collars, calendar spreads and ratio spreadsratio spreads
Profit equations and graphs for option combination Profit equations and graphs for option combination strategies including straddles and box spreadsstrategies including straddles and box spreads
Chance/Brooks An Introduction to Derivatives and Risk Management, 9th ed. Ch. 7: 4
Option Spreads: Basic Concepts (continued)
Why Investors Use Option SpreadsWhy Investors Use Option Spreads Risk reductionRisk reduction To lower the cost of a long positionTo lower the cost of a long position Types of spreadsTypes of spreads
bull spreadbull spread bear spreadbear spread time spread is based on volatilitytime spread is based on volatility
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Money Spreads (continued)
Bull Spreads (continued)Bull Spreads (continued) For different holding periods, compute profit for range For different holding periods, compute profit for range
of stock prices at Tof stock prices at T11, T, T22, and T using Black-Scholes-, and T using Black-Scholes-
Merton model. See Merton model. See Figure 7.2.. Note how time value decay affects profit for given Note how time value decay affects profit for given
holding period.holding period. Early exercise not a problem.Early exercise not a problem.
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Money Spreads (continued)
Bear Spreads (continued)Bear Spreads (continued) For different holding periods, compute profit for range For different holding periods, compute profit for range
of stock prices at Tof stock prices at T11, T, T22, and T using Black-Scholes-, and T using Black-Scholes-
Merton model. See Merton model. See Figure 7.4.. Note how time value decay affects profit for given Note how time value decay affects profit for given
holding period.holding period. Note early exercise problem.Note early exercise problem.
A Note About Put Money SpreadsA Note About Put Money Spreads Can construct call bear and put bull spreads.Can construct call bear and put bull spreads.
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Money Spreads (continued)
CollarsCollars Buy stock, buy put with strike XBuy stock, buy put with strike X11, sell call with strike , sell call with strike
XX22. N. NSS = 1, N = 1, NPP = 1, N = 1, NCC = -1. = -1. Profit equation: Profit equation: = S = STT - S - S00 + Max(0,X + Max(0,X11 - S - STT) - P) - P11 - -
Max(0,SMax(0,STT - X - X22) + C) + C22
= X= X11 - S - S00 - P - P11 + C + C22 if S if STT X X11 < X < X22
= S= STT - S - S00 - P - P11 + C + C22 if X if X11 < S < STT < X < X22
= X= X22 - S - S00 - P - P11 + C + C2 2 if Xif X11 < X < X22 S STT
A common type of collar is what is often referred to as A common type of collar is what is often referred to as a zero-cost collar. The call strike is set such that the a zero-cost collar. The call strike is set such that the call premium offsets the put premium so that there is no call premium offsets the put premium so that there is no initial outlay for the options.initial outlay for the options.
See See Figure 7.5 for DCRB July 120/136.165, PP11 = $13.65, C = $13.65, C22 = $13.65. That is, a call strike of = $13.65. That is, a call strike of 136.165 generates the same premium as a put with 136.165 generates the same premium as a put with strike of 120. This result can be obtained only by strike of 120. This result can be obtained only by using an option pricing model and plugging in using an option pricing model and plugging in exercise prices until you find the one that makes the exercise prices until you find the one that makes the call premium the same as the put premium. call premium the same as the put premium.
This will nearly always require the use of OTC This will nearly always require the use of OTC options.options.
Maximum profit = XMaximum profit = X22 - S - S00. Minimum = X. Minimum = X11 - S - S00.. Breakeven: SBreakeven: STT
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Money Spreads (continued)
Collars (continued)Collars (continued) The collar is a lot like a bull spread The collar is a lot like a bull spread
(compare (compare Figure 7.5 to to Figure 7.1).). The collar payoff exceeds the bull spread payoff by The collar payoff exceeds the bull spread payoff by
the difference between Xthe difference between X11 and the interest on X and the interest on X11.. Thus, the collar is equivalent to a bull spread plus a Thus, the collar is equivalent to a bull spread plus a
risk-free bond paying Xrisk-free bond paying X11 at expiration. at expiration.
For different holding periods, compute profit for range For different holding periods, compute profit for range of stock prices at Tof stock prices at T11, T, T22, and T using Black-Scholes-, and T using Black-Scholes-
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Money Spreads (continued)
Butterfly SpreadsButterfly Spreads Buy call with strike XBuy call with strike X11, buy call with strike X, buy call with strike X33, sell two calls , sell two calls
with strike Xwith strike X22. Let N. Let N11 = 1, N = 1, N22 = -2, N = -2, N33 = 1. = 1. Profit equation: Profit equation: = Max(0,S = Max(0,STT - X - X11) - C) - C11
- 2Max(0,S- 2Max(0,STT - X - X22) + 2C) + 2C22 + Max(0,S + Max(0,STT - X - X33) - C) - C33
= -C= -C11 + 2C + 2C22 - C - C3 3 if Sif STT X X11 < X < X22 < X < X33
= S= STT - X - X11 - C - C11 + 2C + 2C22 - C - C33 if X if X11 < S < STT X X22 < X < X33
= -S= -STT +2X +2X22 - X - X11 - C - C11 + 2C + 2C22 - C - C33 if Xif X11 < X < X22 < S < STT X X33
= -X= -X11 + 2X + 2X22 - X - X33 - C - C11 + 2C + 2C22 - C - C33 if Xif X11 < X < X22 < X < X33 < S < STT
See See Figure 7.7 for DCRB July 120/125/130, C for DCRB July 120/125/130, C11 = $16.00, = $16.00, CC22 = $13.50, C = $13.50, C33 = $11.35. = $11.35.
Maximum profit = XMaximum profit = X22 - X - X11 - C - C11 + 2C + 2C22 - C - C33, , minimum = -Cminimum = -C11 + 2C + 2C22 - C - C33
Breakeven: SBreakeven: STT** = X = X11 + C + C11 - 2C - 2C22 + C + C33 and and
SSTT* = 2X* = 2X22 - X - X11 - C - C11 + 2C + 2C22 - C - C33
For different holding periods, compute profit for range of For different holding periods, compute profit for range of stock prices at Tstock prices at T11, T, T22, and T using Black-Scholes-Merton , and T using Black-Scholes-Merton model. See model. See Figure 7.8..
Note how time value decay affects profit for given Note how time value decay affects profit for given holding period.holding period.
Note early exercise problem.Note early exercise problem.
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Calendar Spreads
Buy call with longer time to expiration, sell call with Buy call with longer time to expiration, sell call with shorter time to expiration.shorter time to expiration.
Note how this strategy cannot be held to expiration Note how this strategy cannot be held to expiration because there are two different expirations.because there are two different expirations.
Profitability depends on volatility and time value Profitability depends on volatility and time value decay.decay.
Use Black-Scholes-Merton model to value options at Use Black-Scholes-Merton model to value options at end of holding period if prior to expiration.end of holding period if prior to expiration.
See See Figure 7.9.. Note time value decay. See Note time value decay. See Table 7.2 and and Figure 7.10.. Early exercise can be problem.Early exercise can be problem. Can be constructed with puts as well.Can be constructed with puts as well.
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Ratio Spreads
Long one option, short another based on deltas of two Long one option, short another based on deltas of two options. Designed to be delta-neutral. Can use any two options. Designed to be delta-neutral. Can use any two options on same stock.options on same stock.
Portfolio valuePortfolio value V = NV = N11CC11 + N + N22CC22
Set to zero and solve for NSet to zero and solve for N11/N/N22 = - = -22//11, which is , which is ratio of their deltas (recall that ratio of their deltas (recall that = N(d1) from Black-Scholes-Merton model).
Buy June 120s, sell June 125s. Delta of 120 is 0.630; Buy June 120s, sell June 125s. Delta of 120 is 0.630; delta of 125 is 0.569. Ratio is –(0.569/0.630) = -0.903. delta of 125 is 0.569. Ratio is –(0.569/0.630) = -0.903. For example, buy 903 June 120s, sell 1,000 June 125sFor example, buy 903 June 120s, sell 1,000 June 125s
Note why this works and that delta will change.Note why this works and that delta will change. Why do this? Hedging mispriced optionWhy do this? Hedging mispriced option
Chance/Brooks An Introduction to Derivatives and Risk Management, 9th ed. Ch. 7: 17
Straddles
Straddle: long an equal number of puts and callsStraddle: long an equal number of puts and calls Profit equation: Profit equation: = Max(0,ST - X) - C
+ Max(0,X - ST) - P (assuming Nc = 1, Np = 1) = ST - X - C - P if ST X = X - ST - C - P if ST < X
Either call or put will be exercised (unless SEither call or put will be exercised (unless STT = X). = X). See See Figure 7.11 for DCRB June 125, for DCRB June 125,
C = $13.50, P = $11.50.C = $13.50, P = $11.50. Breakeven: SBreakeven: STT
** = X - C - P and S = X - C - P and STT** = X + C + P = X + C + P
Maximum profit: Maximum profit: , minimum = - C - P, minimum = - C - P See See Figure 7.12 for different holding periods. Note time for different holding periods. Note time
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Straddles (continued)
Applications of StraddlesApplications of Straddles Based on perception of volatility greater than priced by Based on perception of volatility greater than priced by
marketmarket A Short StraddleA Short Straddle
Unlimited loss potentialUnlimited loss potential Based on perception of volatility less than priced by Based on perception of volatility less than priced by
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Box Spreads (continued)
Evaluate by determining net present value (NPV)Evaluate by determining net present value (NPV) NPV = (XNPV = (X22 - X - X11)(1 + r))(1 + r)-T-T - C - C11 + C + C22 - P - P22 + P + P11
This determines whether present value of risk-free This determines whether present value of risk-free payoff exceeds initial value of transaction.payoff exceeds initial value of transaction.
If NPV > 0, do it. If NPV < 0, do the reverse.If NPV > 0, do it. If NPV < 0, do the reverse. See See Figure 7.13.. Box spread is also difference between two put-call Box spread is also difference between two put-call
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Box Spreads (continued)
Evaluate June 125/130 box spreadEvaluate June 125/130 box spread Buy 125 call at $13.50, sell 130 call at $11.35Buy 125 call at $13.50, sell 130 call at $11.35 Buy 130 put at $14.25, sell 125 put at $11.50Buy 130 put at $14.25, sell 125 put at $11.50 Initial outlay = $4.90, $490 for 100 eachInitial outlay = $4.90, $490 for 100 each NPV = 100[(130 - 125)(1.0456)NPV = 100[(130 - 125)(1.0456)-0.0959-0.0959 - 4.90] - 4.90]
= 7.85= 7.85 NPV > 0 so do itNPV > 0 so do it
Early exercise a problem only on short box spreadEarly exercise a problem only on short box spread Transaction costs highTransaction costs high
