Consider a chooser option (also known as an as-you-like-it option) on a nondividend-paying stock. At time 1, its holder will choose whether it becomes a European call option or a European put option, each of which will expire at time 3 with a strike price of $100. The chooser option price is $20 at time t 0. The stock price is $95 at time t = 0. Let C(T) denote the price of a European call option at time t = 0 on the stock expiring at time T, T 0, with a strike price of $100.
You are given:
(i) The risk-free interest rate is 0.
(ii) C(1) $4.
Determine C(3).