Compound Options. Consider a stock that is currently worth 100. Every month, the stock price either increases by a factor 1.02 with probability .53 or it decreases by a factor 0.99 with probability.47. The interest rate is constant at 1% (monthly compounding). Consider an American put option with a strike price of 100 that expires after three months. Compute the arbitrage-free price of this option Consider now a call on put (COP) option which provides its owner the right (but not the obligation) to buy the American put option from part 3a in 2 months from now at a strike price K' = 1. Compute the arbitrage-free price of the COP option. Consider now a put on put (POP) option which gives its holder the right (but not the obligation) to sell the American put option from part 3a in two months from now at a strike price K' = 1. Derive first a put-call parity formula for CoP and PoP options and then use this formula together with the result of part 3b to compute the value of the PoP option. Compound Options. Consider a stock that is currently worth 100. Every month, the stock price either increases by a factor 1.02 with probability .53 or it decreases by a factor 0.99 with probability.47. The interest rate is constant at 1% (monthly compounding). Consider an American put option with a strike price of 100 that expires after three months. Compute the arbitrage-free price of this option Consider now a call on put (COP) option which provides its owner the right (but not the obligation) to buy the American put option from part 3a in 2 months from now at a strike price K' = 1. Compute the arbitrage-free price of the COP option. Consider now a put on put (POP) option which gives its holder the right (but not the obligation) to sell the American put option from part 3a in two months from now at a strike price K' = 1. Derive first a put-call parity formula for CoP and PoP options and then use this formula together with the result of part 3b to compute the value of the PoP option