a Consider a non-dividend paying stock with a current stock price is $45, where the volatility of the stock price is 30% per annum and the risk free rate is 5% per annum. Using a binomial tree with a step length of one month, calculate the following: a) u, d, and the risk neutral probability p for the tree. P b) The value of a European call option on the stock, both with a strike price of 42.50 and a time to maturity of three months. c) The value of a European put option and an American put option on the stock, both with a strike price of 42.50 and a time to maturity of three months. Also calculate the early exercise premium. d) Verify that the put call parity holds for the European options. a a a a a a a Consider a non-dividend paying stock with a current stock price is $45, where the volatility of the stock price is 30% per annum and the risk free rate is 5% per annum. Using a binomial tree with a step length of one month, calculate the following: a) u, d, and the risk neutral probability p for the tree. P b) The value of a European call option on the stock, both with a strike price of 42.50 and a time to maturity of three months. c) The value of a European put option and an American put option on the stock, both with a strike price of 42.50 and a time to maturity of three months. Also calculate the early exercise premium. d) Verify that the put call parity holds for the European options. a a a a a a