Financial Mathematics:

6. Consider a CRR model with T-2, S0-$100. Sl = $200 or S1 = $50 (the same model as in Exercise 2). Now consider an American put option with strike price K $120. Assume that the risk free interest rate is -0.1 a) Use a binary tree to compute the arbitrage free initial price of the American put option. (b) Determine an explicit superhedging strategy * for this option. (c) Suppose that you can buy the American put option at time zero for S1 less than its arbitrage free price. Explicitly describe a strategy that yields an arbitrage opportunity for a buyer of the American put option. (d) Try to automate the arbitrage free pricing of an American put option in a computer program where T, So, u, d and K are variables 6. Consider a CRR model with T-2, S0-$100. Sl = $200 or S1 = $50 (the same model as in Exercise 2). Now consider an American put option with strike price K $120. Assume that the risk free interest rate is -0.1 a) Use a binary tree to compute the arbitrage free initial price of the American put option. (b) Determine an explicit superhedging strategy * for this option. (c) Suppose that you can buy the American put option at time zero for S1 less than its arbitrage free price. Explicitly describe a strategy that yields an arbitrage opportunity for a buyer of the American put option. (d) Try to automate the arbitrage free pricing of an American put option in a computer program where T, So, u, d and K are variables