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## Chapter 6: Basic Option Strategies

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**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.**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.**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.**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.**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.**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.**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.**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.**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.**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.**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.**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.**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.**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.**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.**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.**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.**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.**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.**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.**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.**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.**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.**Summary**Software Demonstration 6.1 shows the Excel spreadsheet stratlyz3.xls for analyzing option strategies. An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.**(Return to text slide)**An Introduction to Derivatives and Risk Management, 6th ed.