Suppose that over two periods a stock price moves on a binomial tree:

(a) Find an arbitrage opportunity when the riskless rate equals $1 / 10$. Give precise details of when and how much you buy, borrow and sell.

(b) From here on, assume instead that the riskless rate equals $1 / 4$. Determine the equivalent martingale measure. [No proof is required.]

(c) Determine the time-zero price of an American put with strike 15 and expiry 2 . Assume you sell it at this price. Which hedge do you put on at time zero? Consider the scenario of two bad periods. How does your hedge work?

(d) The buyer of the American put turns out to be an unsophisticated investor who fails to use his early exercise right when he should. Assume the first period was bad. How much profit can you make out of this? You should detail your exact strategy.