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Question

2. The buyer of a European put option has the right to sell a certain stock to the seller of the put option at a strike price K at time t 1. Initially at t 0, the stock price is S, which can either rise to us or drop to ds at time t 1, where u 1 and d 1. Assume that dS K us. The interest rate is r for the time period.

(a) Construct a A hedging portfolio to price the put option.

(b) Argue that the put option price you derived is arbitrage free.

(c) Compute is the risk-neutral probability.

(d) Show that the price you derived in (a) is the present value of the expected payoff of the option under the risk-neutral probability.