Consider a nondividend 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:

1)u, d, and the risk neutral probability p for the tree.

20The 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.

3)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 time value and the early exercise premium.

4)Verify that the put call parity holds for the European options.

show work in excel