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 $18.

The chooser option price is $6 at time t = 0. The stock price is $20 at time t = 0.

Let C(T) and P(T) denote, respectively, the prices of a European call option and a European put option at time t = 0 on the stock expiring at time T, T > 0, with a strike price of $18.

You are given:

(i) The continuously compounded risk-free interest rate is 0.

(ii) P(1) = $1.04.

(iii) C(3) = $4.33.

Describe actions you could take at times t = 0 and t = 1 only using the chooser option and the options in (ii) and (iii) to exploit an arbitrage opportunity. Verify carefully that your trading strategy is indeed an arbitrage, i.e., your cash flows at all times are always non-negative and sometimes strictly positive.