chapter 7: advanced option strategies read every book by traders to study where they lost money. you...

Chapter 7: Advanced Option Chapter 7: Advanced Option StrategiesStrategies

Read every book by traders to study where they lost money. You will learn nothing relevant from their profits (the markets adjust). You will learn from their losses.

Nassim TalebDerivatives Strategy, April, 1997, p. 25

Chance/BrooksChance/BrooksAn Introduction to Derivatives and Risk Management, 9th ed.

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© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Important Concepts in Chapter 7Important Concepts in Chapter 7Profit equations and graphs for option

spread strategies, including money spreads, collars, calendar spreads and ratio spreads

Profit equations and graphs for option combination strategies including straddles and box spreads


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Option Spreads: Basic ConceptsOption Spreads: Basic Concepts◦Definitions

spread vertical, strike, money spread horizontal, time, calendar spread

spread notation June 120/125 June/July 120

long or short long, buying, debit spread short, selling, credit spread


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Option Spreads: Basic Concepts Option Spreads: Basic Concepts (continued)(continued)Why Investors Use Option Spreads◦Risk reduction◦To lower the cost of a long position◦Types of spreads

bull spread bear spread time spread is based on volatility


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Option Spreads: Basic Concepts Option Spreads: Basic Concepts (continued)(continued)Notation◦For money spreads

X1 < X2 < X3

C1, C2, C3

N1, N2, N3

◦For time spreads T1 < T2

C1, C2

N1, N2

◦See Table 7.1 for DCRB option data


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Money SpreadsMoney SpreadsBull Spreads◦Buy call with strike X1, sell call with strike X2. Let

N1 = 1, N2 = -1◦Profit equation: = Max(0,ST - X1) - C1 -

Max(0,ST - X2) + C2 = -C1 + C2 if ST X1 < X2

= ST - X1 - C1 + C2 if X1 < ST X2

= X2 - X1 - C1 + C2 if X1 < X2 < ST

See Figure 7.1 for DCRB June 125/130, C1 = $13.50, C2 = $11.35.

◦Maximum profit = X2 - X1 - C1 + C2, Minimum = - C1 + C2

◦Breakeven: ST* = X1 + C1 - C2


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Money Spreads (continued)Money Spreads (continued)Bull Spreads (continued)◦For different holding periods, compute profit

for range of stock prices at T1, T2, and T using Black-Scholes-Merton model. See Figure 7.2.

◦Note how time value decay affects profit for given holding period.

◦Early exercise not a problem.


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Money Spreads (continued)Money Spreads (continued)

4) One way to create a bull spread positions is by purchasing a low strike call option and selling a high strike call option. Identify a strategy with put options that creates a similar bull spread-shaped profit profile.


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Money Spreads (continued)Money Spreads (continued)Bear Spreads◦Buy put with strike X2, sell put with strike X1. Let

N1 = -1, N2 = 1◦Profit equation: = -Max(0,X1 - ST) + P1

+ Max(0,X2 - ST) - P2

= X2 - X1 + P1 - P2 if ST X1 < X2

= P1 + X2 - ST - P2 if X1 < ST < X2

= P1 - P2 if X1 < X2 ST

See Figure 7.3 for DCRB June 130/125, P1 = $11.50, P2 = $14.25.

Maximum profit = X2 - X1 + P1 - P2. Minimum = P1 - P2.

Breakeven: ST* = X2 + P1 - P2.


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Money Spreads (continued)Money Spreads (continued)Bear Spreads (continued)◦For different holding periods, compute profit

for range of stock prices at T1, T2, and T using Black-Scholes-Merton model. See Figure 7.4.


◦Note early exercise problem.A Note About Put Money Spreads◦Can construct call bear and put bull spreads.


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6) Construct a bear money spread using the October 165 and 170 calls. Hold the position until the options expire. Determine the profits and graph the results. Identify the breakeven stock price at expiration and the maximum and minimum profits. Discuss any special considerations associated with

this strategy.


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Money Spreads (continued)Money Spreads (continued)Collars◦Buy stock, buy put with strike X1, sell call with strike

X2. NS = 1, NP = 1, NC = -1.◦Profit equation: = ST - S0 + Max(0,X1 - ST) - P1 -

Max(0,ST - X2) + C2

= X1 - S0 - P1 + C2 if ST X1 < X2

= ST - S0 - P1 + C2 if X1 < ST < X2

= X2 - S0 - P1 + C2 if X1 < X2 ST

◦A common type of collar is what is often referred to as a zero-cost collar. The call strike is set such that the call premium offsets the put premium so that there is no initial outlay for the options.


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Money Spreads (continued)Money Spreads (continued)Collars (continued)

See Figure 7.5 for DCRB July 120/136.165, P1 = $13.65, C2 = $13.65. That is, a call strike of 136.165 generates the same premium as a put with strike of 120. This result can be obtained only by using an option pricing model and plugging in exercise prices until you find the one that makes the call premium the same as the put premium.

This will nearly always require the use of OTC options.

Maximum profit = X2 - S0. Minimum = X1 - S0. Breakeven: ST

* = S0.


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Money Spreads (continued)Money Spreads (continued)Collars (continued)◦The collar is a lot like a bull spread

(compare Figure 7.5 to Figure 7.1). The collar payoff exceeds the bull spread payoff by

the difference between X1 and the interest on X1. Thus, the collar is equivalent to a bull spread plus a

risk-free bond paying X1 at expiration.

◦For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black-Scholes-Merton model. See Figure 7.6.


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21) Explain conceptually the choice of strike prices when it comes to designing a zero-cost collar. Specifically, address the costs and benefits of two strategies. One strategy has a higher put strike price than the second strategy.


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Money Spreads (continued)Money Spreads (continued)Butterfly Spreads◦Buy call with strike X1, buy call with strike X3, sell

two calls with strike X2. Let N1 = 1, N2 = -2, N3 = 1.◦Profit equation: = Max(0,ST - X1) - C1

- 2Max(0,ST - X2) + 2C2 + Max(0,ST - X3) - C3 = -C1 + 2C2 - C3 if ST X1 < X2 < X3

= ST - X1 - C1 + 2C2 - C3 if X1 < ST X2 < X3

= -ST +2X2 - X1 - C1 + 2C2 - C3 if X1 < X2 < ST X3

= -X1 + 2X2 - X3 - C1 + 2C2 - C3 if X1 < X2 < X3 < ST

See Figure 7.7 for DCRB July 120/125/130, C1 = $16.00, C2 = $13.50, C3 = $11.35.


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Money Spreads (continued)Money Spreads (continued)Butterfly Spreads (continued)◦Maximum profit = X2 - X1 - C1 + 2C2 - C3,

minimum = -C1 + 2C2 - C3

◦Breakeven: ST* = X1 + C1 - 2C2 + C3 and

ST* = 2X2 - X1 - C1 + 2C2 - C3

◦For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black-Scholes-Merton model. See Figure 7.8.


◦Note early exercise problem.


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Calendar SpreadsCalendar Spreads◦Buy call with longer time to expiration, sell call

with shorter time to expiration.◦Note how this strategy cannot be held to expiration

because there are two different expirations.◦Profitability depends on volatility and time value

decay.◦Use Black-Scholes-Merton model to value options

at end of holding period if prior to expiration.◦See Figure 7.9.◦Note time value decay. See Table 7.2 and

Figure 7.10.◦Can be constructed with puts as well.◦Butterfly spreads & Calendar spreads are volatility

strategies


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Calendar SpreadsCalendar Spreads22) Pear, Inc., is presently trading at $100 per share; atthe-money one-month calls are trading at $5.43, and puts are trading at $5.01; and at-the-money two-month calls are trading at $7.72, and puts are trading at $6.89. At present, these option prices reflect a Black-Scholes-Merton implied volatility of 45 percent for all options. You believe, however, that the volatility over the next month will be lower than 45 percent and the volatility in the second month will be higher than 45 percent because you think Pear, Inc., will publicly scheduled an earnings announcement in 45 days and there will be an information blackout period leading up to the announcement. A blackout period occurs when a company does not provide any information to the public for a stated period of time. The earnings announcement will cause higher volatility, and the blackout period will result in lower volatility. Design an option strategy using all four options that will profit if you are correct in your volatility belief, the company publicly schedules the announcement within the next few days, and option prices immediately adjust to these beliefs.


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Ratio SpreadsRatio Spreads◦Long one option, short another based on deltas of

two options. Designed to be delta-neutral. Can use any two options on same stock.

◦Portfolio value V = N1C1 + N2C2

Set to zero and solve for N1/N2 = -2/1, which is 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; delta of 125 is 0.569. Ratio is –(0.569/0.630) = -0.903. For example, buy 903 June 120s, sell 1,000 June 125s

◦Note why this works and that delta will change.◦Why do this? Hedging mispriced option


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StraddlesStraddles◦Straddle: long an equal number of puts and calls◦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 ST = X).◦See Figure 7.11 for DCRB June 125,

C = $13.50, P = $11.50.◦Breakeven: ST

* = X - C - P and ST* = X + C + P

◦Maximum profit: , minimum = - C - P◦See Figure 7.12 for different holding periods. Note

time value decay.


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Straddles (continued)Straddles (continued)Applications of Straddles◦Based on perception of volatility greater than

priced by marketA Short Straddle◦Unlimited loss potential◦Based on perception of volatility less than

priced by market


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Straddles (continued)Straddles (continued)

16) A strip is a variation of a straddle involving two puts and one call. Construct a short strip using the August 170 options. Hold the position until the options expire. Determine the profits and graph the results. Identify the breakeven stock prices at expiration and the minimum profit.


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Straddles (continued)Straddles (continued)

23) Another variation of the straddle is called a strangle. A strangle is the purchase of a call with a higher exercise price and a put with a lower exercise price. Evaluate the strangle strategy by examining the purchase of the August 165 put and 170 call. Determine the profits for stock prices of 150, 155, 160, 165, 170, 175, and 180. Hold the position until expiration and graph the results. Find the breakeven stock prices at expiration. Explain why one would want to use a strangle.


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Box SpreadsBox Spreads◦ Definition: bull call money spread plus bear put money spread.

Risk-free payoff if options are European

◦ Construction: Buy call with strike X1, sell call with strike X2

Buy put with strike X2, sell put with strike X1

◦ Profit equation: = Max(0,ST - X1) - C1 - Max(0,ST - X2) + C2 + Max(0,X2 - ST) - P2 - Max(0,X1 - ST) + P1

= X2 - X1 - C1 + C2 - P2 + P1 if ST X1 < X2

= X2 - X1 - C1 + C2 - P2 + P1 if X1 < ST X2

= X2 - X1 - C1 + C2 - P2 + P1 if X1 < X2 ST


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Box Spreads (continued)Box Spreads (continued)

◦Evaluate by determining net present value (NPV) NPV = (X2 - X1)(1 + r)-T - C1 + C2 - P2 + P1

This determines whether present value of risk-free payoff exceeds initial value of transaction.

If NPV > 0, do it. If NPV < 0, do the reverse.

◦See Figure 7.13.◦Box spread is also difference between two

put-call parities.


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Box Spreads (continued)Box Spreads (continued)

◦Evaluate June 125/130 box spread Buy 125 call at $13.50, sell 130 call at $11.35 Buy 130 put at $14.25, sell 125 put at $11.50 Initial outlay = $4.90, $490 for 100 each NPV = 100[(130 - 125)(1.0456)-0.0959 - 4.90]

= 7.85 NPV > 0 so do it

◦Early exercise a problem only on short box spread

◦Transaction costs high


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SummarySummary


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My ProblemsMy Problems

◦4 Bull Spread◦6 Bear Spread◦16 Straddle◦21 Collar◦22 Calendar Spread◦23 Straddle


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TAProblemsTAProblems

◦7 Bear Spread◦9 Butterfly Spread◦12 Box Spread◦17 Box Spread◦15 Straddle◦24 Money, Calendar Spread


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chapter 7: advanced option strategies read every book by traders to study where they lost money. you...

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