D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 1 Chapter 6: Basic Option Strategies I’m not a seat-of-the-pants person, and options trading is a seat-of-the-pants business. Elizabeth Mackay Women of the Street (by Sue Herera), 1997, p. 25

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 2 Important Concepts in Chapter 6 n Profit equations and graphs for buying and selling stock, buying and selling calls, buying and selling puts, covered calls, protective puts and conversions/reversals n The effect of choosing different exercise prices n The effect of closing out an option position early versus holding to expiration

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 3 Terminology and Notation n Note the following standard symbols u C = current call price, P = current put price u S 0 = current stock price, S T = stock price at expiration u T = time to expiration u X = exercise price    = profit from strategy n The number of calls, puts and stock is given as u N C = number of calls u N P = number of puts u N S = number of shares of stock

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 4 Terminology and Notation (continued) n These symbols imply the following: u N C, N P, or N S > 0 implies buying (going long) u N C, N P, or N S < 0 implies selling (going short) n The Profit Equations u Profit equation for calls held to expiration   = N C [Max(0,S T - X) - C] For buyer of one call (N C = 1) this implies  = Max(0,S T - X) - CFor buyer of one call (N C = 1) this implies  = Max(0,S T - X) - C For seller of one call (N C = -1) this implies  = -Max(0,S T - X) + C For seller of one call (N C = -1) this implies  = -Max(0,S T - X) + C

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 5 Terminology and Notation (continued) n The Profit Equations (continued) u Profit equation for puts held to expiration   = N P [Max(0,X - S T ) - P] For buyer of one put (N P = 1) this implies  = Max(0,X - S T ) - PFor buyer of one put (N P = 1) this implies  = Max(0,X - S T ) - P For seller of one put (N P = -1) this implies  = -Max(0,X - S T ) + PFor seller of one put (N P = -1) this implies  = -Max(0,X - S T ) + P

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 6 Terminology and Notation (continued) n The Profit Equations (continued) u Profit equation for stock   = N S [S T - S 0 ] For buyer of one share (N S = 1) this implies  = S T - S 0For buyer of one share (N S = 1) this implies  = S T - S 0 For short seller of one share (N S = -1) this implies  = -S T + S 0For short seller of one share (N S = -1) this implies  = -S T + S 0

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 7 Terminology and Notation (continued) n Different Holding Periods u Three holding periods: T 1 < T 2 < T u For a given stock price at the end of the holding period, compute the theoretical value of the option using the Black-Scholes or other appropriate model. F Remaining time to expiration will be either T - T 1, T - T 2 or T - T = 0 (we have already covered the latter) F For a position closed out at T 1, the profit will be F where the closeout option price is taken from the Black-Scholes model for a given stock price at T 1.

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 8 Terminology and Notation (continued) n Different Holding Periods (continued) u Similar calculation done for T 2 u For T, the profit is determined by the intrinsic value, as already covered n Assumptions u No dividends u No taxes or transaction costs u We continue with the AOL options. See Table 6.1, p Table 6.1, p. 197Table 6.1, p. 197

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 9 Stock Transactions n Buy Stock  Profit equation:  Profit equation:  = N S [S T - S 0 ] given that N S > 0 u u See Figure 6.1, p. 198 for AOL, S 0 = $ Figure 6.1, p. 198 u u Maximum profit = , minimum = -S 0 n Sell Short Stock  Profit equation:  Profit equation:  = N S [S T - S 0 ] given that N S < 0 u u See Figure 6.2, p. 199 for AOL, S 0 = $ Figure 6.2, p. 199 u u Maximum profit = S 0, minimum = - 

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 10 Call Option Transactions n Buy a Call  Profit equation:  = N C [Max(0,S T - X) - C] given that N C > 0. Letting N C = 1,   = S T - X - C if S T > X   = - C if S T  X u See Figure 6.3, p. 200 for AOL June 125, C = $13.50 Figure 6.3, p. 200Figure 6.3, p. 200 u Maximum profit =, minimum = -C u Maximum profit = , minimum = -C u Breakeven stock price found by setting profit equation to zero and solving: S T * = X + C

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 11 Call Option Transactions (continued) n Buy a Call (continued) u See Figure 6.4, p. 201 for different exercise prices. Note differences in maximum loss and breakeven. Figure 6.4, p. 201Figure 6.4, p. 201 u For different holding periods, compute profit for range of stock prices at T 1, T 2, and T using Black-Scholes model. See Table 6.2, p. 202 and Figure 6.5, p Table 6.2, p. 202Figure 6.5, p. 203Table 6.2, p. 202Figure 6.5, p. 203 u Note how time value decay affects profit for given holding period.

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 12 Call Option Transactions (continued) n Write a Call  Profit equation:  = N C [Max(0,S T - X) - C] given that N C < 0. Letting N C = -1,   = -S T + X + C if S T > X   = C if S T  X u See Figure 6.6, p. 205 for AOL June 125, C = $13.50 Figure 6.6, p. 205Figure 6.6, p. 205 u Maximum profit = +C, minimum = - u Maximum profit = +C, minimum = -  u Breakeven stock price same as buying call: S T * = X + C

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 13 Call Option Transactions (continued) n Write a Call (continued) u See Figure 6.7, p. 206 for different exercise prices. Note differences in maximum loss and breakeven. Figure 6.7, p. 206Figure 6.7, p. 206 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 6.8, p Figure 6.8, p. 207Figure 6.8, p. 207 u Note how time value decay affects profit for given holding period.

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 14 Put Option Transactions n Buy a Put  Profit equation:  = N P [Max(0,X - S T ) - P] given that N P > 0. Letting N P = 1,   = X - S T - P if S T < X   = - P if S T  X u See Figure 6.9, p. 208 for AOL June 125, P = $11.50 Figure 6.9, p. 208Figure 6.9, p. 208 u Maximum profit = X - P, minimum = -P u Breakeven stock price found by setting profit equation to zero and solving: S T * = X - P

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 15 Put Option Transactions (continued) n Buy a Put (continued) u See Figure 6.10, p. 209 for different exercise prices. Note differences in maximum loss and breakeven. Figure 6.10, p. 209Figure 6.10, p. 209 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 6.11, p Figure 6.11, p. 210Figure 6.11, p. 210 u Note how time value decay affects profit for given holding period.

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 16 Put Option Transactions (continued) n Write a Put  Profit equation:  = N P [Max(0,X - S T )- P] given that N P < 0. Letting N P = -1   = -X + S T + P if S T < X   = P if S T  X u See Figure 6.12, p. 211 for AOL June 125, P = $11.50 Figure 6.12, p. 211Figure 6.12, p. 211 u Maximum profit = +P, minimum = -X + P u Breakeven stock price found by setting profit equation to zero and solving: S T * = X - P

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 17 Put Option Transactions (continued) n Write a Put (continued) u See Figure 6.13, p. 212 for different exercise prices. Note differences in maximum loss and breakeven. Figure 6.13, p. 212Figure 6.13, p. 212 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 6.14, p Figure 6.14, p. 213Figure 6.14, p. 213 u Note how time value decay affects profit for given holding period. n Figure 6.15, p. 214 summarizes these payoff graphs. Figure 6.15, p. 214 Figure 6.15, p. 214

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 18 Calls and Stock: the Covered Call u One short call for every share owned  Profit equation:  = N S (S T - S 0 ) + N C [Max(0,S T - X) - C] given N S > 0, N C 0, N C < 0, N S = -N C. With N S = 1, N C = -1,   = S T - S 0 + C if S T X   = S T - S 0 + C if S T  X   = X - S 0 + C if S T > X u See Figure 6.16, p. 215 for AOL June 125, S 0 = $ , C = $13.50 Figure 6.16, p. 215Figure 6.16, p. 215 u Maximum profit = X - S 0 + C, minimum = -S 0 + C u Breakeven stock price found by setting profit equation to zero and solving: S T * = S 0 - C

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 19 Calls and Stock: the Covered Call (continued) u See Figure 6.17, p. 216 for different exercise prices. Note differences in maximum loss and breakeven. Figure 6.17, p. 216Figure 6.17, p. 216 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 6.18, p Figure 6.18, p. 217Figure 6.18, p. 217 u Note the effect of time value decay. u Some General Considerations for Covered Calls: F alleged attractiveness of the strategy F misconception about picking up income F rolling up to avoid exercise u Opposite is short stock, buy call

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 20 Puts and Stock: the Protective Put u One long put for every share owned  Profit equation:  = N S (S T - S 0 ) + N P [Max(0,X - S T ) - P] given N S > 0, N P > 0, N S = N P. With N S = 1, N P = 1,   = S T - S 0 - P if S T X   = S T - S 0 - P if S T  X   = X - S 0 - P if S T < X u See Figure 6.19, p. 220 for AOL June 125, S 0 = $ , P = $11.50 Figure 6.19, p. 220Figure 6.19, p. 220 u Maximum profit =, minimum = X - S 0 - P u Maximum profit = , minimum = X - S 0 - P u Breakeven stock price found by setting profit equation to zero and solving: S T * = P + S 0 u Like insurance policy

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 21 Puts and Stock: the Protective Put (continued) u See Figure 6.20, p. 221 for different exercise prices. Note differences in maximum loss and breakeven. Figure 6.20, p. 221Figure 6.20, p. 221 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 6.21, p Figure 6.21, p. 224Figure 6.21, p. 224 u Note how time value decay affects profit for given holding period.

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 22 Synthetic Puts and Calls u Rearranging put-call parity to isolate put price u This implies put = long call, short stock, long risk-free bond with face value X. u This is a synthetic put. u In practice most synthetic puts are constructed without risk-free bond, i.e., long call, short stock.

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 23 Synthetic Puts and Calls (continued)  Profit equation:  = N C [Max(0,S T - X) - C] + N S (S T - S 0 ) given that N C > 0, N S 0, N S < 0, N S = N P. Letting N C = 1, N S = -1,   = -C - S T + S 0 if S T X   = -C - S T + S 0 if S T  X   = S 0 - X - C if S T > X u See Figure 6.22, p. 225 for synthetic put vs. actual put. Figure 6.22, p. 225Figure 6.22, p. 225 u Table 6.3, p. 226 shows payoffs from reverse conversion (long call, short stock, short put), used when actual put is overpriced. Like risk-free borrowing. Table 6.3, p. 226 Table 6.3, p. 226 u Similar strategy for conversion, used when actual call overpriced.

D. M. ChanceAn Introduction to Derivatives and Risk Management, 6th ed.Ch. 6: 24 Summary Software Demonstration 6.1 shows the Excel spreadsheet stratlyz3.xls for analyzing option strategies.

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