Modify your formulas from (1) to compute the price at time 0 of an American put option with the same contract speci cations in the binomial model. Report the price of the American put option under the binomial model.

Compute x(1); y(1) i.e., the number of shares of the stock and risk-free asset needed at time 0 to replicate the American option over the rst time-step.

Identify which nodes (if any) prior to the terminal date T = 1 are optimal exercise points. In other words, identify the points on the binomial tree, if any, where early exercise is optimal. It is enough to simply highlight these nodes on a visual representation of the stock or option price binomial tree.

Report the early exercise premium for the American put option, i.e., compute PA PE. This is the cash value associated with the ability to exercise early.