期权 期货以及其他衍生品-8.pptVIP

Properties ofStock Option PricesChapter 8 Notation c : European call option price p : European put option price S0 : Stock price today K : Strike price T : Life of option s: 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抯 life r : Risk-free rate for maturity T with cont comp Effect of Variables on Option Pricing (Table 8.1, page 168) c p C P Variable S0 K T s r D + + ? + ? ? + + + + + + + ? + ? ? ? ? + ? + ? + American vs European Options An American option is worth at least as much as the corresponding European option C ?c P ?p Calls: An Arbitrage Opportunity? Suppose that c = 3 S0 = 20 T = 1 r = 10% K = 18 D = 0 Is there an arbitrage opportunity? Lower Bound for European Call Option Prices; No Dividends (Equation 8.1, page 173) c ?S0 朘e -rT Puts: An Arbitrage Opportunity? Suppose that p = 1 S0 = 37 T = 0.5 r =5% K = 40 D = 0 Is there an arbitrage opportunity? Lower Bound for European Put Prices; No Dividends (Equation 8.2, page 174) p ?Ke-rT朣0 Put-Call Parity; No Dividends (Equation 8.3, page 174) Consider the following 2 portfolios: Portfolio A: European call on a stock + PV of the strike price in cash Portfolio C: European put on the stock + the stock Both are worth MAX(ST , K ) at the maturity of the options They must therefore be worth the same today This means that c + Ke -rT = p + S0 Arbitrage Opportunities Suppose that c = 3 S0 = 31 T = 0.25 r = 10% K =30 D = 0 What are the arbitrage possibilities when p = 2.25 ? p = 1 ? Early Exercise Usually there is some chance that an American option will be exercised early An exception is an American call on a non-dividend paying stock This should never be exercised early F