Let Tc < T and K > 0 be given, a chooser option is a contract sold at time zero that confers on its owner the right to receive either a European call or a put time time Tc. The owner of the chooser option may wait until time Tc before choosing. The European call or put chosen expires at time T with strike price K. (a) (3 points) Let ct and pt be the European call and put prices at time t. Write down the value of the chooser option at time Tc. (b) (12 points) Let r be the annual continuously compounding interest rate. Show that the time-zero price of a chooser option is the sum of the timezero price of a put, expiring at time T and having strike price K, and a call, expiring at time Tc and having strike price Ker(T Tc) . (Hint: use put-call parity at time Tc.)