Assume a European chooser option where stock price is $10, strike price is $10, volatility is 20%, dividend yield is 0%, and risk-free rate is 4%. The choice can be made within the next six months (T1 = 0.5 years) and the option will expire in one year (T2 = 1.0 year). What is a synthetic (portfolio) equivalent to the chooser option?
答案是：A call option with strike price 10 and maturity 1 year and a put option with strike price 9.8 and maturity 0.5 year.
选择期权在t1选择什么应该取决于当时价格。根据F=s*e^（tr），如果当时价格小于10*e^-（0.4*0.5），会选择是put，如果大于会选择call。也就是当半年过去了，价格大于9.8，你会拥有一个call，（replication也是在价格大于9.8时，拥有一个 call，put无用）。小于9.8你会拥有一个put。（replication是这个时候你short了一个股票+long a call=一个put，可画pay off图得出）
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