Chapter 6: Basic Option Strategies

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 An Introduction to Derivatives and Risk Management, 6th ed.

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

3. Terminology and Notation • Note the following standard symbols • C = current call price, P = current put price • S0 = current stock price, ST = stock price at expiration • T = time to expiration • X = exercise price • P = profit from strategy • The number of calls, puts and stock is given as • NC = number of calls • NP = number of puts • NS = number of shares of stock An Introduction to Derivatives and Risk Management, 6th ed.

4. Terminology and Notation (continued) • These symbols imply the following: • NC,NP, or NS > 0 implies buying (going long) • NC, NP, or NS < 0 implies selling (going short) • The Profit Equations • Profit equation for calls held to expiration • P = NC[Max(0,ST - X) - C] • For buyer of one call (NC = 1) this implies P = Max(0,ST - X) - C • For seller of one call (NC = -1) this implies P = -Max(0,ST - X) + C An Introduction to Derivatives and Risk Management, 6th ed.

5. Terminology and Notation (continued) • The Profit Equations (continued) • Profit equation for puts held to expiration • P = NP[Max(0,X - ST) - P] • For buyer of one put (NP = 1) this implies P = Max(0,X - ST) - P • For seller of one put (NP = -1) this implies P = -Max(0,X - ST) + P An Introduction to Derivatives and Risk Management, 6th ed.

6. Terminology and Notation (continued) • The Profit Equations (continued) • Profit equation for stock • P = NS[ST - S0] • For buyer of one share (NS = 1) this implies P = ST - S0 • For short seller of one share (NS = -1) this implies P = -ST + S0 An Introduction to Derivatives and Risk Management, 6th ed.

7. Terminology and Notation (continued) • Different Holding Periods • Three holding periods: T1 < T2 < T • 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. • Remaining time to expiration will be either T - T1, T - T2 or T - T = 0 (we have already covered the latter) • For a position closed out at T1, the profit will be • where the closeout option price is taken from the Black-Scholes model for a given stock price at T1. An Introduction to Derivatives and Risk Management, 6th ed.

8. Terminology and Notation (continued) • Different Holding Periods (continued) • Similar calculation done for T2 • For T, the profit is determined by the intrinsic value, as already covered • Assumptions • No dividends • No taxes or transaction costs • We continue with the AOL options. See Table 6.1, p. 197. An Introduction to Derivatives and Risk Management, 6th ed.

9. Stock Transactions • Buy Stock • Profit equation: P = NS[ST - S0] given that NS > 0 • See Figure 6.1, p. 198 for AOL, S0 = $125.9375 • Maximum profit = , minimum = -S0 • Sell Short Stock • Profit equation: P = NS[ST - S0] given that NS < 0 • See Figure 6.2, p. 199 for AOL, S0 = $125.9375 • Maximum profit = S0, minimum = -  An Introduction to Derivatives and Risk Management, 6th ed.

10. Call Option Transactions • Buy a Call • Profit equation: P = NC[Max(0,ST - X) - C] given that NC > 0. Letting NC = 1, • P = ST - X - C if ST > X • P = - C if ST£ X • See Figure 6.3, p. 200 for AOL June 125, C = $13.50 • Maximum profit = , minimum = -C • Breakeven stock price found by setting profit equation to zero and solving: ST* = X + C An Introduction to Derivatives and Risk Management, 6th ed.

11. Call Option Transactions (continued) • Buy a Call (continued) • See Figure 6.4, p. 201 for different exercise prices. Note differences in maximum loss and breakeven. • For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black-Scholes model. See Table 6.2, p. 202 and Figure 6.5, p. 203. • Note how time value decay affects profit for given holding period. An Introduction to Derivatives and Risk Management, 6th ed.

12. Call Option Transactions (continued) • Write a Call • Profit equation: P = NC[Max(0,ST - X) - C] given that NC < 0. Letting NC = -1, • P = -ST + X + C if ST > X • P = C if ST£ X • See Figure 6.6, p. 205 for AOL June 125, C = $13.50 • Maximum profit = +C, minimum = -  • Breakeven stock price same as buying call: ST* = X + C An Introduction to Derivatives and Risk Management, 6th ed.

13. Call Option Transactions (continued) • Write a Call (continued) • See Figure 6.7, p. 206 for different exercise prices. Note differences in maximum loss and breakeven. • For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black-Scholes model. See Figure 6.8, p. 207. • Note how time value decay affects profit for given holding period. An Introduction to Derivatives and Risk Management, 6th ed.

14. Put Option Transactions • Buy a Put • Profit equation: P = NP[Max(0,X - ST) - P] given that NP > 0. Letting NP = 1, • P = X - ST - P if ST < X • P = - P if ST³ X • See Figure 6.9, p. 208 for AOL June 125, P = $11.50 • Maximum profit = X - P, minimum = -P • Breakeven stock price found by setting profit equation to zero and solving: ST* = X - P An Introduction to Derivatives and Risk Management, 6th ed.

15. Put Option Transactions (continued) • Buy a Put (continued) • See Figure 6.10, p. 209 for different exercise prices. Note differences in maximum loss and breakeven. • For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black-Scholes model. See Figure 6.11, p. 210. • Note how time value decay affects profit for given holding period. An Introduction to Derivatives and Risk Management, 6th ed.

16. Put Option Transactions (continued) • Write a Put • Profit equation: P = NP[Max(0,X - ST)- P] given that NP < 0. Letting NP = -1 • P = -X + ST + P if ST < X • P = P if ST³ X • See Figure 6.12, p. 211 for AOL June 125, P = $11.50 • Maximum profit = +P, minimum = -X + P • Breakeven stock price found by setting profit equation to zero and solving: ST* = X - P An Introduction to Derivatives and Risk Management, 6th ed.

17. Put Option Transactions (continued) • Write a Put (continued) • See Figure 6.13, p. 212 for different exercise prices. Note differences in maximum loss and breakeven. • For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black-Scholes model. See Figure 6.14, p. 213. • Note how time value decay affects profit for given holding period. • Figure 6.15, p. 214 summarizes these payoff graphs. An Introduction to Derivatives and Risk Management, 6th ed.

18. Calls and Stock: the Covered Call • One short call for every share owned • Profit equation: P = NS(ST - S0) + NC[Max(0,ST - X) - C] given NS > 0, NC < 0, NS = -NC. With NS = 1, NC = -1, • P = ST - S0 + C if ST£ X • P = X - S0 + C if ST > X • See Figure 6.16, p. 215 for AOL June 125, S0 = $125.9375, C = $13.50 • Maximum profit = X - S0 + C, minimum = -S0 + C • Breakeven stock price found by setting profit equation to zero and solving: ST* = S0 - C An Introduction to Derivatives and Risk Management, 6th ed.

19. Calls and Stock: the Covered Call (continued) • See Figure 6.17, p. 216 for different exercise prices. Note differences in maximum loss and breakeven. • For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black-Scholes model. See Figure 6.18, p. 217. • Note the effect of time value decay. • Some General Considerations for Covered Calls: • alleged attractiveness of the strategy • misconception about picking up income • rolling up to avoid exercise • Opposite is short stock, buy call An Introduction to Derivatives and Risk Management, 6th ed.

20. Puts and Stock: the Protective Put • One long put for every share owned • Profit equation: P = NS(ST - S0) + NP[Max(0,X - ST) - P] given NS > 0, NP > 0, NS = NP. With NS = 1, NP = 1, • P = ST - S0 - P if ST³ X • P = X - S0 - P if ST < X • See Figure 6.19, p. 220 for AOL June 125, S0 = $125.9375, P = $11.50 • Maximum profit = , minimum = X - S0 - P • Breakeven stock price found by setting profit equation to zero and solving: ST* = P + S0 • Like insurance policy An Introduction to Derivatives and Risk Management, 6th ed.

21. Puts and Stock: the Protective Put (continued) • See Figure 6.20, p. 221for different exercise prices. Note differences in maximum loss and breakeven. • For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black-Scholes model. See Figure 6.21, p. 224. • Note how time value decay affects profit for given holding period. An Introduction to Derivatives and Risk Management, 6th ed.

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

23. Synthetic Puts and Calls (continued) • Profit equation: P = NC[Max(0,ST - X) - C] + NS(ST - S0) given that NC > 0, NS < 0, NS = NP. Letting NC = 1, NS = -1, • P = -C - ST + S0 if ST£ X • P = S0 - X - C if ST > X • See Figure 6.22, p. 225 for synthetic put vs. actual put. • 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. • Similar strategy for conversion, used when actual call overpriced. An Introduction to Derivatives and Risk Management, 6th ed.

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

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