restrictionsonoptionsprices(衍生金融工具-人民-wenkub
2023-03-05 05:29:12 本頁面
【正文】 ce value bond that matures at T Exercise (strike) price Value of a European call Value of an American call Value of a European put Value of a American put T T S(t) B(t,T)=er(Tt) K (or X) c(S,K,t,T) C(S,K,t,T) p(S,K,t,T) P(S,K,t,T) ? Basic Intuition Effect on the price of a stock option of increasing one variable while keeping all others fixed: Variable European Call European Put American Call American Put Stock price Strike price Time to expiration Volatility Riskfree rate Dividends ? Basic arbitrage relations: Note: The following restrictions hold regardless of whether the underlying stock pays dividends or not. A. A call is never worth more than the stock and a put is never worth more than exercise price C(S,K,t,T) ?S(t) c(S,K,t,T) ?S(t) P(S,K,t,T) ?K p(S,K,t,T) ?K B. European puts are never worth more than the present value of the exercise price. p(S,K,t,T) ?KB(t,T)K . Intuitively, this has to hold since th timeT payoff to European put holder is bounded (from above) by K. C. Options never has a negative value: C(S,K,t,T)?0 c(S,K,t,T)?0 P(S,K,t,T)?0 p(S,K,t,T)?0 D. American options are at least as valuable as European options: C(S,K,t,T)?c(S,K,t,T) P(S,K,t,T)?p(S,K,t,T) E. American options with more time to maturity are at least as valuable。 ., if CP SPV(D)K Transaction Initial (t) Cash flow Final (T) Cash flow S(T) K S(T) K Write a call Buy a put Buy a stock Borrow KB C P S KB CP (SKB) 0 KS(T) S(T)+D K D [S(T)K] 0 S(T)+D K D then we can have the following arbitrage: Question: We have only shown that the strategy is an arbitrage if your portfolio is held until maturity. What if the written put is exercised against you before maturity? Transaction Initial (t) Cash flow Final (T) Cash flow S(T) K S(T)K C P S K PV(D) 0 [KS(T)] (S(T)+D) Ker(Tt) D S(T)K 0 (S(T)+D) Ker(Tt) D [SPV(D)K] [CP] ?0 ?0 ? Summary A. Arbitrage opportunities cannot exist in effi
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