2. Suppose the price of a stock is currently $50. Over each of the two next 3 month periods it is expected to go up by 6% or down by 5%. Suppose the risk-free interest rate is 5% per annum with continuous compounding. (a) Find the price of a 6 month European call option with a strike price of $51. In making your calculations, draw a figure of the event-tree with the prices of the stock and the call option at each node. (b) Find the price of a 6 month European put option with the same strike price and draw a figure of the event-tree with the prices of the stock and put option at each node. (c) Verify that the above put and call prices satisfy the put-call parity relation. (d) If the put option were American would it ever be optimal to exercise it early at any of the nodes of the event-tree? 2. Suppose the price of a stock is currently $50. Over each of the two next 3 month periods it is expected to go up by 6% or down by 5%. Suppose the risk-free interest rate is 5% per annum with continuous compounding. (a) Find the price of a 6 month European call option with a strike price of $51. In making your calculations, draw a figure of the event-tree with the prices of the stock and the call option at each node. (b) Find the price of a 6 month European put option with the same strike price and draw a figure of the event-tree with the prices of the stock and put option at each node. (c) Verify that the above put and call prices satisfy the put-call parity relation. (d) If the put option were American would it ever be optimal to exercise it early at any of the nodes of the event-tree