restrictionsonoptionsprices(衍生金融工具-人民-文庫吧在線文庫
【正文】 rican call option between exdividend dates or prior to maturity. ||| Today(t) Exdividend Maturity Date (?) of Option (T) Consider two strategies: i. Exercise the option now, value is S(t)K ii. Wait till just before the exdividend date and exercise for sure, even if the option is outofthemoney. The value of the strategy at ? is Sc(?)K, where Sc(?) is the cumstock price just before the stock goes dividend. Hence the value of this strategy today is S(t)KB(t,?). What can you say? 2. The option will be exercised just prior to the exdividend date if, and only if, the exercise value exceeds the no exercise value, that is Se(?)+dK C(Se(?),K,?,T), where Se(?) is exdividendday stock price. American Puts 1. As it is pointed out earlier it may be optimal to early exercise American put option, even if the underlying stock pays no dividends. 2. Dividends will tend to delay early exercise of an American put option. It never pays to early exercise an American put option just prior to an exdividend date. Consider two strategies: i. Exercise the put option just before the exdivided date. The value of he option is: K(Se+d) ii. Exercise the put option just after the exdividend date. The value is KSe. C. PutCall Parity for European calls on stock with known dividend S(t)=c(S,K,t,T)p(S,K,t,T)+KB(t,T)+PV(D) D. What39。 ., 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
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