You are given the following information on a European Call Option. The option matures in 0.5 years and is at the money. The current stock price of the underlying stock is $60.00. Assume that the stock can either go up or down by 15% per period. Set up a replicating portfolio of the stock and a risk free bond and use a one-period binomial model. The risk free rate is 5.0% per year:

a) Show CLEARLY the payoffs for the Stock, Bond and the Call.

b) Calculate the Number of Stocks and Bonds in both periods required to replicate the call.

c) Using no Arbitrage, compute the price of the Call option using this replicating portfolio.

d) Compute the probability that the stock price will go up.

e) Then use the probability to compute the annualized sigma of the stock.

f) Compute the Black- Scholes- theoretical option price for a European Call option on the stock.

g) Using Put Call Parity, compute the price of a European Put option on a share of the stock. Please answer all parts clearly and concisely. Thank you