6. A standard chooser option (or called as-you-like-it option) entitles the holder to choose, at a predetermined time T in the future, whether the T0-maturity option is a standard European call or put with a common strike price K for the remaining time to expiration ToT. The payoff of the chooser option on the date of choice T is V(ST,T)=max(CE(ST,T;K,To),PE(ST,T;K,To)), where CE(ST,T;K,To) and PE(ST,T;K,To) are the European call and put option prices with strike price K and maturity To, respectively, at time T with stock price ST. (a) Show that the chooser option is equivalent to the combination of one call (with strike price K1 and maturity T1 ) and x units of put (with strike price K2 and maturity T2 ). Specify K1,T1,x,K2, and T2. (b) Use the Black-Scholes formula to give the value of the chooser option at time t, where tT