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Stock Options and Trading Strategies

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

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  1. Stock Options and Trading Strategies Finance (Derivative Securities) 312 Tuesday, 12 September 2006 Readings: Chapters 9 & 10

  2. 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

  3. Variable S0 K ? ? T  r D Factors Influencing Value c p C P – – + + – – + + + + + + + + – – + + – – + +

  4. 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)

  5. Upper and Lower Bounds • Suppose that c = 3 S0= 20 T= 1 r= 10% K = 18 D= 0 • Is there an arbitrage opportunity?

  6. Upper and Lower Bounds • Lower Bound for European Call Options • cS0 –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

  7. Upper and Lower Bounds • Suppose that p = 1 S0 = 37 T = 0.5 r = 5% K = 40 D = 0 • Is there an arbitrage opportunity?

  8. Upper and Lower Bounds • Lower Bound for European Put Options • pKe–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

  9. 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

  10. 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

  11. 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

  12. American Options • Early exercise of calls (non-dividend paying) • Insurance • Time value • Early exercise of puts (non-dividend paying) • Insurance worth forgoing

  13. 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

  14. 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

  15. Bull Spread using Calls Profit ST K1 • K2

  16. Profit K1 K2 ST Bull Spread using Puts

  17. Bear Spread using Calls Profit K1 K2 ST

  18. Profit K1 K2 ST Bear Spread using Puts

  19. Calendar Spread using Calls Profit ST K

  20. Calendar Spread using Puts Profit ST K

  21. 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

  22. 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

  23. Protective Put Profit Stock 48 Protective Put 48 50 53 55 0 ST -2 -5 Put Option Breakeven point -50

  24. 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)

  25. 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

  26. Covered Call Profit Stock Breakeven point 15 Covered Call 5 0 ST 45 50 60 65 -45 Call Option -50

  27. 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

  28. Long Straddle Profit Long Call Breakeven points Long Straddle X 0 ST Long Put

  29. Short Straddle Profit Short Put 0 X ST Short Straddle Breakeven points Short Call

  30. 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

  31. Long Strangle Profit Long Call Breakeven points Long Strangle XP XC 0 ST Long Put

  32. Short Strangle Profit Short Put XP XC ST 0 Short Strangle Breakeven points Long Call

  33. 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

  34. Strip Profit Long Call Breakeven points Strip X 0 ST Long Put x 2

  35. Strap Profit Long Call x 2 Breakeven points Strap X 0 ST Long Put

  36. 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)

  37. Butterfly Spread Profit Long Put X1 Long Call X3 X1 X3 0 ST X2 Butterfly Breakeven points Short Put X2 Short Call X2

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