Exercise 2.12 (Chooser option). Let 1 sm SN - 1 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 call or a put at time m. The owner of the chooser may wait until time m before choosing. The call or put chosen expires at time N with strike price K. Show that the time-zero price of a chooser option is the sum of the time-zero price of a put, expiring at time N and having strike price K, and a call, expiring at time m and having strike price (1+". (Hint: m Use put call parity (Exercise 2.11).) K