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).

(A) $ 9

(B) $11

(C) $13

(D) $15

(E) $17