Chapter 11 Properties of Stock Options. Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull
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1 Chapter 11 Properties of Stock Options 1
2 Notation c: European call option price p: European put option price S 0 : Stock price today K: Strike price T: Life of option σ: Volatility of stock price C: American call option price P: American put option price S T : Stock price at option maturity D: PV of dividends paid during life of option r Risk-free rate for maturity T with cont. comp. 2
3 Effect of Variables on Option Pricing (Table 11.1, page 235) Variable c p C P S K + + T?? + + σ r + + D + + 3
4 American vs European Options An American option is worth at least as much as the corresponding European option C c P p 4
5 Calls: An Arbitrage Opportunity?! Suppose that c = 3 S 0 = 20 T = 1 r = 10% K = 18 D = 0! Is there an arbitrage opportunity? 5
6 Lower Bound for European Call Option Prices; No Dividends (Equation 11.4, page 240) c max(s 0 Ke rt, 0) 6
7 Puts: An Arbitrage Opportunity?! Suppose that p= 1 S 0 = 37 T = 0.5 r =5% K = 40 D = 0! Is there an arbitrage opportunity? 7
8 Lower Bound for European Put Prices; No Dividends (Equation 11.5, page 241) p max(ke -rt S 0, 0) 8
9 Put-Call Parity: No Dividends! Consider the following 2 portfolios:! Portfolio A: European call on a stock + zerocoupon bond that pays K at time T! Portfolio C: European put on the stock + the stock 9
10 Values of Portfolios S T > K S T < K Portfolio A Call option S T K 0 Zero-coupon bond K K Total S T K Portfolio C Put Option 0 K S T Share S T S T Total S T K 10
11 The Put-Call Parity Result (Equation 11.6, page 242)! Both are worth max(s T, K ) at the maturity of the options! They must therefore be worth the same today. This means that c + Ke -rt = p + S 0 11
12 Arbitrage Opportunities! Suppose that c= 3 S 0 = 31 T = 0.25 r = 10% K =30 D = 0! What are the arbitrage possibilities when p = 2.25? p = 1? 12
13 Early Exercise! Usually there is some chance that an American option will be exercised early! An exception is an American call on a nondividend paying stock! This should never be exercised early 13
14 An Extreme Situation! For an American call option: S 0 = 100; T = 0.25; K = 60; D = 0 Should you exercise immediately?! What should you do if! You want to hold the stock for the next 3 months?! You do not feel that the stock is worth holding for the next 3 months? 14
15 Reasons For Not Exercising a Call Early (No Dividends)! No income is sacrificed! You delay paying the strike price! Holding the call provides insurance against stock price falling below strike price 15
16 Bounds for European or American Call Options (No Dividends) 16
17 Should Puts Be Exercised Early? Are there any advantages to exercising an American put when S 0 = 60; T = 0.25; r=10% K = 100; D = 0 17
18 Bounds for European and American Put Options (No Dividends) 18
19 The Impact of Dividends on Lower Bounds to Option Prices (Equations 11.8 and 11.9, page 249) c S 0 D Ke rt p D + Ke rt S 0 19
20 Extensions of Put-Call Parity! American options; D = 0 S 0 K < C P < S 0 Ke rt Equation 11.7 p. 244! European options; D > 0 c + D + Ke rt = p + S 0 Equation p. 250! American options; D > 0 S 0 D K < C P < S 0 Ke rt Equation p
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