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Stock Options and Trading Strategies. Finance (Derivative Securities) 312 Tuesday, 12 September 2006 Readings: Chapters 9 & 10. Notation. c : European call option price p : European put option price S 0 : Stock price today K : Strike price T : Life of option
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Stock Options and Trading Strategies Finance (Derivative Securities) 312 Tuesday, 12 September 2006 Readings: Chapters 9 & 10
Notation • c : European call option price • p : European put option price • S0: Stock price today • K : Strike price • T : Life of option • : Volatility of stock price • C : American Call option price • P : American Put option price • ST: Stock price at option maturity • D : Present value of dividends during option’s life • r: Risk-free rate for maturity Twith cont comp
Variable S0 K ? ? T r D Factors Influencing Value c p C P – – + + – – + + + + + + + + – – + + – – + +
Upper and Lower Bounds • Call Options • Stock price is upper bound for both American and European • Put Options • Exercise price is upper bound for both American and European (PV of K)
Upper and Lower Bounds • Suppose that c = 3 S0= 20 T= 1 r= 10% K = 18 D= 0 • Is there an arbitrage opportunity?
Upper and Lower Bounds • Lower Bound for European Call Options • cS0 –Ke –rT (non-dividend paying) • Since S0 –Ke –rT= $3.71, and c = $3, opportunity for arbitrage exists • Short stock, buy call, invest proceeds • If stock price > $18, profit = $0.79 • If stock price < $18, profit = $1.79
Upper and Lower Bounds • Suppose that p = 1 S0 = 37 T = 0.5 r = 5% K = 40 D = 0 • Is there an arbitrage opportunity?
Upper and Lower Bounds • Lower Bound for European Put Options • pKe–rT – S0(non-dividend paying) • Since Ke–rT – S0= $2.01, and p = $1, opportunity for arbitrage exists • Borrow p + S0, buy stock, repay loan • If stock price < $40, profit = $1.04 • If stock price > $40, profit = $3.04
Put-Call Parity • Consider strategy I: Buy a share, and buy a put option ST≤ K ST> K Buy Stock ST ST Buy Put K – ST 0 Total K ST
Put-Call Parity • Consider strategy II: Buy a call option, and borrow Ke–rT ST≤ K ST > K Buy Call 0ST – K Invest Ke–rTKK Total K ST
Put-Call Parity • If two portfolios provide the same return, they must cost the same to set up, otherwise an opportunity for arbitrage exists p + S0 = c + Ke–rT
American Options • Early exercise of calls (non-dividend paying) • Insurance • Time value • Early exercise of puts (non-dividend paying) • Insurance worth forgoing
Effect of Dividends • Consider strategy I: Buy a put, a share, and borrow D + Ke–rT ST≤ K ST> K Buy Share STST Buy Put K – ST0 Borrow D+Ke-rT–K–K Total 0 ST – K
Effect of Dividends • Consider strategy II: Buy a call ST≤ K ST> K Buy Call 0ST – K Total 0 ST – K p + S0 = c + D + Ke–rT
Bull Spread using Calls Profit ST K1 • K2
Profit K1 K2 ST Bull Spread using Puts
Bear Spread using Calls Profit K1 K2 ST
Profit K1 K2 ST Bear Spread using Puts
Calendar Spread using Calls Profit ST K
Calendar Spread using Puts Profit ST K
Protective Put • Buy stock, worth $50 • Buy put option, exercise price $53, premium $5 • Used when the investor is worried the stock price will fall • Put option provides insurance against loss on the stock
Protective Put At expiry: ST Payoff (Stock + Put) Profit 45 -5 + 8 = 3 3 - 5 = -2 50 0 + 3 = 3 3 - 5 = -2 55 5 + 0 = 5 5 - 5 = 0 60 10 + 0 = 10 10 - 5 = 5 65 15 + 0 = 15 15 - 5 = 10 70 20 + 0 = 20 20 - 5 = 15
Protective Put Profit Stock 48 Protective Put 48 50 53 55 0 ST -2 -5 Put Option Breakeven point -50
Covered Call • Buy stock, worth $50 • Write call option, exercise price $60, premium $5 • Used to boost income with premiums collected, and locks in a selling price (though potential capital gains are forfeited)
Covered Call At expiry: ST Payoff Profit 30 -20 -15 40 -10 -5 50 0 5 60 10 15 70 10 15 80 10 15
Covered Call Profit Stock Breakeven point 15 Covered Call 5 0 ST 45 50 60 65 -45 Call Option -50
Straddles • Buy call and put with same exercise price • Used when share price is expected to move, but direction uncertain • For short straddle, sell call and put
Long Straddle Profit Long Call Breakeven points Long Straddle X 0 ST Long Put
Short Straddle Profit Short Put 0 X ST Short Straddle Breakeven points Short Call
Strangles • Buy out-of-the-money call and put, where XC > XP • Similar to straddle, but price needs to move by greater amount in order to breakeven • Costs less than straddle • For short strangle, sell call and put
Long Strangle Profit Long Call Breakeven points Long Strangle XP XC 0 ST Long Put
Short Strangle Profit Short Put XP XC ST 0 Short Strangle Breakeven points Long Call
Strips and Straps • Strip is a bearish straddle • Buy 2 puts and 1 call with same X • Strap is a bullish straddle • Buy 1 put and 2 calls with same X
Strip Profit Long Call Breakeven points Strip X 0 ST Long Put x 2
Strap Profit Long Call x 2 Breakeven points Strap X 0 ST Long Put
Butterfly Spread • Buy put option with relatively low exercise price (X1) • Buy call option with a relatively high exercise price (X3) • Sell a put option and a call option with an exercise price between X1 and X3 (X2)
Butterfly Spread Profit Long Put X1 Long Call X3 X1 X3 0 ST X2 Butterfly Breakeven points Short Put X2 Short Call X2