Consider the 3 period binomial model with a risk-free asset A with A(0) = 20, interest rate r = 0.07 and a stock S with S(0) = 10, "up" return u = 0.1 and "down" return d so that (1+d)(1+u) = 1.

An American call option with expiration date 3 gives the owner the right but not obligation to buy stock at the strike price. In contrast to the European call, the owner of the option has the right to exercise the option at any one of the times 0, 1, 2, 3. We consider a call with strike price 10

1. Compute the non-discounted stock price process S(0), S(1), S(2), S(3).

2. The intrinsic value process G(0), ..., G(3) is defined as G(t) = S(t) STRIKE. Compute it.

3. An investor owns this option and decides to exercise it at the following times: Immediately after observing ₁=u (that is, at time 1); immediately after observing ₁₂=du (that is, at time 2); after observing ₁₂₃=ddu (that is, at time 3); otherwise, he lets the option expire. Determine the resulting cash flow process.