properties of option prices缩减.ppt

* Chapter 8　 Properties ofStock Option Prices * 8.1 factors affecting options prices 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 T with cont comp Notation * Effect of Variables on Option Pricing c p C P Variable S0 K T ? + + – + ? ? + + + + + + – – – + * 8.2 basic option price relationship under no arbitrage condition An American option is worth at least as much as the corresponding European option C ? c P ? p upper and lower bounds for option prices Upper bounds Call options: Put options: * 8.2 basic option price relationship under no arbitrage condition upper and lower bounds for option prices Lower bond for European calls on no-dividend-paying stocks Suppose:S0=$20,K=$18,r=10%per annum, T=1year * Continued. Formal prove: Portfolio A: one European call option plus an amount of cash equal to Portfolio B: one share At time T: A is worth: B is worth: ST Under no arbitrage condition, today: * upper and lower bounds for option prices Lower bond for European puts on no-dividend-paying stocks 8.2 basic option price relationship under no arbitrage condition * Continued. Formal prove: Portfolio C: one European put option plus one share Portfolio D: an amount of cash equal to At time T: C is worth: D is worth: K Under no arbitrage condition, today: * Continued. Suppose p=$1. Is there an arbitrage opportunity? Suppose:S0=$37, X=$40, r=5%per annum, T=0.5year * Put-Call Parity for European options Portfolio A: one European call option plus an amount of cash equal to Portfolio C: one European put option plus one share Both are worth at expiration date. European options; under no arbitrage condition : portfolios A and C must ha