We consider a binomial tree with only one step. The risk-free interest rate is r = 0.08, the continuous dividend rate is = 0.03, and the time interval corresponding to the step we take is h = 1/2. The option expires at time t = h. The current stock price is S = 100. We construct a portfolio consisting of shares of the stock and the amount B in a risk-free bond with interest rate r. We assume that u = e (r)h+ h and d = e (r)h h , where = 0.35. We consider a European put option with strike price K = 98.

(a) (Determine the numerical values of u and d, and of uS and dS. Also determine the numerical values of the payoffs Cu and Cd at time h. Use two decimal places for uS, dS, Cu, and Cd, but more decimals for u and d so that the two decimals in the other four answers are certainly correct. Show your work.

(b) Using only symbols and no numbers, write down the two equations that the stock-bond portfolio is required to satisfy (that one solves to determine and B, not the final formulas for and B). It suffices to give the answer.

(c) ) Either directly from a formula, or after determining the numerical values of and B, find the numerical value of the put option price at the present time. Use two decimal places for the option price. Show your work.