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Copyright © 2001 by Harcourt, Inc. All rights reserved.1 Chapter 7: Advanced Option Strategies You can get as fancy as you want with your option strategies, but in this business, there’s no substitute for being right. There’s never been a guarantee for incremental returns. Gene Brody Risk, June 1995

Copyright © 2001 by Harcourt, Inc. All rights reserved.5 Option Spreads: Basic Concepts (continued) n Notation u For money spreads F X 1 < X 2 < X 3 F C 1, C 2, C 3 F N 1, N 2, N 3 u For time spreads F T 1 < T 2 F C 1, C 2 F N 1, N 2 u See Table 7.1, p. 265 for America Online option data

Copyright © 2001 by Harcourt, Inc. All rights reserved.6 Money Spreads n Bull Spreads u Buy call with strike X 1, sell call with strike X 2. Let N 1 = 1, N 2 = -1  Profit equation:  = Max(0,S T - X 1 ) - C 1 - Max(0,S T - X 2 ) + C 2   = -C 1 + C 2 if S T X 1 < X 2   = -C 1 + C 2 if S T  X 1 < X 2   = S T - X 1 - C 1 + C 2 if X 1 < S T X 2   = S T - X 1 - C 1 + C 2 if X 1 < S T  X 2   = X 2 - X 1 - C 1 + C 2 if X 1 < X 2 < S T F See Figure 7.1, p. 267 for AOL June 125/130, C 1 = \$13.50, C 2 = \$11.375. u Maximum profit = X 2 - X 1 - C 1 + C 2, Minimum = - C 1 + C 2 u Breakeven: S T * = X 1 + C 1 - C 2

Copyright © 2001 by Harcourt, Inc. All rights reserved.7 Money Spreads (continued) n Bull Spreads (continued) u For different holding periods, compute profit for range of stock prices at T 1, T 2 and T using Black-Scholes model. See Figure 7.2, p. 269. u Note how time value decay affects profit for given holding period. u Early exercise not a problem.

Copyright © 2001 by Harcourt, Inc. All rights reserved.8 Money Spreads (continued) n Bear Spreads u Buy put with strike X 2, sell put with strike X 1. Let N 1 = -1, N 2 = 1  Profit equation:  = -Max(0,X 1 - S T ) + P 1 + Max(0,X 2 - S T ) - P 2   = X 2 - X 1 + P 1 - P 2 if S T X 1 < X 2   = X 2 - X 1 + P 1 - P 2 if S T  X 1 < X 2   = P 1 + X 2 - S T - P 2 if X 1 < S T < X 2   = P 1 - P 2 if X 1 < X 2  S T F See Figure 7.3, p. 271 for AOL June 130/125, P 1 = \$11.50, P 2 = \$14.25. F Maximum profit = X 2 - X 1 + P 1 - P 2. Minimum = P 1 - P 2. F Breakeven: S T * = X 2 + P 1 - P 2.

Copyright © 2001 by Harcourt, Inc. All rights reserved.9 Money Spreads (continued) n Bear Spreads (continued) u For different holding periods, compute profit for range of stock prices at T 1, T 2 and T using Black-Scholes model. See Figure 7.4, p. 272. u Note how time value decay affects profit for given holding period. u Note early exercise problem. n A Note About Put Money Spreads u Can construct call bear and put bull spreads.

Copyright © 2001 by Harcourt, Inc. All rights reserved.10 Money Spreads (continued) n Collars u Buy stock, buy put with strike X 1, sell call with strike X 2. N S = 1, N P = 1, N C = -1.  Profit equation:  = S T - S 0 + Max(0,X 1 - S T ) - P 1 - Max(0,S T - X 2 ) + C 2   = X 1 - S 0 - P 1 + C 2 if S T X 1 < X 2   = X 1 - S 0 - P 1 + C 2 if S T  X 1 < X 2   = S T - S 0 - P 1 + C 2 if X 1 < S T < X 2   = X 2 - S 0 - P 1 + C 2 if X 1 < X 2  S T u 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.

Copyright © 2001 by Harcourt, Inc. All rights reserved.11 Money Spreads (continued) n Collars (continued) F See Figure 7.5, p. 275 for AOL June 120/136.23, P 1 = \$13.625, C 2 = \$13.625. That is, a call strike of 136.23 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. F This will nearly always require the use of OTC options. F Maximum profit = X 2 - S 0. Minimum = X 1 - S 0. F Breakeven: S T * = S 0.

Copyright © 2001 by Harcourt, Inc. All rights reserved.12 Money Spreads (continued) n Collars (continued) u The collar is a lot like a bull spread (compare Figure 7.5 to Figure 7.1). F The collar payoff exceeds the bull spread payoff by the difference between X 1 and the interest on X 1. F Thus, the collar is equivalent to a bull spread plus a risk-free bond paying X 1 at expiration. u For different holding periods, compute profit for range of stock prices at T 1, T 2 and T using Black-Scholes model. See Figure 7.6, p. 277.

Copyright © 2001 by Harcourt, Inc. All rights reserved.13 Money Spreads (continued) n Butterfly Spreads u Buy call with strike X 1, buy call with strike X 3, sell two calls with strike X 2. Let N 1 = 1, N 2 = -2, N 3 = 1.  Profit equation:  = Max(0,S T - X 1 ) - C 1 - 2Max(0,S T - X 2 ) + 2C 2 + Max(0,S T - X 3 ) - C 3   = -C 1 + 2C 2 - C 3 if S T X 1 < X 2 < X 3   = -C 1 + 2C 2 - C 3 if S T  X 1 < X 2 < X 3   = S T - X 1 - C 1 + 2C 2 - C 3 if X 1 < S T X 2 < X 3   = S T - X 1 - C 1 + 2C 2 - C 3 if X 1 < S T  X 2 < X 3   = -S T +2X 2 - X 1 - C 1 + 2C 2 - C 3 if X 1 < X 2 < S T X 3   = -S T +2X 2 - X 1 - C 1 + 2C 2 - C 3 if X 1 < X 2 < S T  X 3   = -X 1 + 2X 2 - X 3 - C 1 + 2C 2 - C 3 if X 1 < X 2 < X 3 < S T F See Figure 7.7, p. 280 for AOL July 120/125/130, C 1 = \$16.00, C 2 = \$13.50, C 3 = \$11.375.

Copyright © 2001 by Harcourt, Inc. All rights reserved.14 Money Spreads (continued) n Butterfly Spreads (continued) u Maximum profit = X 2 - X 1 - C 1 + 2C 2 - C 3, minimum = -C 1 + 2C 2 - C 3 u Breakeven: S T * = X 1 + C 1 - 2C 2 + C 3 and S T * = 2X 2 - X 1 - C 1 + 2C 2 - C 3 u For different holding periods, compute profit for range of stock prices at T 1, T 2 and T using Black-Scholes model. See Figure 7.8, p. 281. u Note how time value decay affects profit for given holding period. u Note early exercise problem.

Copyright © 2001 by Harcourt, Inc. All rights reserved.15 Calendar Spreads u Buy call with longer time to expiration, sell call with shorter time to expiration. u Note how this strategy cannot be held to expiration because there are two different expirations. u Profitability depends on volatility and time value decay. u Use Black-Scholes model to value options at end of holding period if prior to expiration. u See Figure 7.9, p. 283. u Note time value decay. See Table 7.2, p. 285 and Figure 7.10, p. 286. u Early exercise can be problem. u Can be constructed with puts as well.

Copyright © 2001 by Harcourt, Inc. All rights reserved.16 Ratio Spreads u Long one option, short another based on deltas of two options. Designed to be delta-neutral. Can use any two options on same stock. u Portfolio value F V = N 1 C 1 + N 2 C 2  Set to zero and solve for N 1 /N 2 = - 2 / 1, which is ratio of their deltas. (recall that  Set to zero and solve for N 1 /N 2 = -  2 /  1, which is ratio of their deltas. (recall that  = N(d 1 ) from Black-Scholes model) u Buy June 125s, sell June 120s. Delta of 120 is.630; delta of 125 is.569. Ratio is -(.569/.630) = -.903. For example, buy 903 June 120s, sell 1,000 June 125s u Note why this works and that delta will change. u Why do this? Hedging mispriced option

Copyright © 2001 by Harcourt, Inc. All rights reserved.17 Straddles, Straps and Strips u Straddle: long an equal number of puts and calls  Profit equation:  Profit equation:  = Max(0,S T - X) - C + Max(0,X - S T ) - P (assuming N c = 1, N p = 1)    = S T - X - C - P if S T  X    = X - S T - C - P if S T < X u Either call or put will be exercised (unless S T = X). u See Figure 7.11, p. 290 for AOL June 125, C = \$13.50, P = \$11.50. u Breakeven: S T * = X - C - P and S T * = X + C + P u Maximum profit: infinite, minimum = - C - P u See Figure 7.12, p. 293 for different holding periods. Note time value decay.

Copyright © 2001 by Harcourt, Inc. All rights reserved.18 Straddles, Straps and Strips (continued) n Applications of Straddles u Based on perception of volatility greater than priced by market n A Short Straddle u Unlimited loss potential u Based on perception of volatility less than priced by market

Copyright © 2001 by Harcourt, Inc. All rights reserved.19 Straddles, Straps and Strips (continued) n Straps u Definition: two long calls and one long put. Doubles up bet on stock going up  Profit equation:  Profit equation:  = 2Max(0,S T - X) - 2C + Max(0,X - S T ) - P (assuming N c = 2, N p = 1)    = 2S T - 2X - 2C - P if S T  X    = X - S T - 2C - P if S T < X u See Figure 7.13, p. 295. u Breakeven: S T * = X + C + P/2 u Maximum profit = infinite, minimum = -2C - P

Copyright © 2001 by Harcourt, Inc. All rights reserved.20 Straddles, Straps and Strips (continued) n Strips u Definition: two long puts and one long call. Doubles up bet on stock going down  Profit equation:  Profit equation:  = Max(0,S T - X) - C + 2Max(0,X - S T ) - 2P (assuming N c = 1, N p = 2)    = S T - X - C - 2P if S T  X    = 2X - 2S T - C - 2P if S T < X u See Figure 7.14, p. 297. u Breakeven: S T * = X - P - C/2 u Maximum profit = infinite, minimum = -2P - C

Copyright © 2001 by Harcourt, Inc. All rights reserved.21 Box Spreads u Definition: bull call money spread plus bear put money spread. Risk-free payoff if options are European u Construction: F Buy call with strike X 1, sell call with strike X 2 F Buy put with strike X 2, sell put with strike X 1  Profit equation:  = Max(0,S T - X 1 ) - C 1 - Max(0,S T - X 2 ) + C 2 + Max(0,X 2 - S T ) - P 2 - Max(0,X 1 - S T ) + P 1   = X 2 - X 1 - C 1 + C 2 - P 2 + P 1 if S T  X 1 < X 2   = X 2 - X 1 - C 1 + C 2 - P 2 + P 1 if X 1 < S T  X 2   = X 2 - X 1 - C 1 + C 2 - P 2 + P 1 if X 1 < X 2  S T

Copyright © 2001 by Harcourt, Inc. All rights reserved.22 Box Spreads (continued) u Evaluate by determining net present value (NPV) F NPV = (X 2 - X 1 )(1 + r) -T - C 1 + C 2 - P 2 + P 1 F This determines whether present value of risk-free payoff exceeds initial value of transaction. F If NPV > 0, do it. If NPV 0, do it. If NPV < 0, do the reverse. u See Figure 7.15, p. 301. u Box spread is also difference between two put-call parities.

Copyright © 2001 by Harcourt, Inc. All rights reserved.23 Box Spreads (continued) u Evaluate June 125/130 box spread F Buy 125 call at \$13.50, sell 130 call at \$11.375 F Buy 130 put at \$14.25, sell 125 put at \$11.50 F Initial outlay = \$4.875, \$487.50 for 100 each F NPV = 100[(130 - 125)(1.0456) -.0959 - 4.875] = 10.37 F NPV > 0 so do it u Early exercise a problem only on short box spread u Transaction costs high