answer only question 4 using model from question 1 !

4. Use the Cox Ross Rubinstein formula and the binomial model described in problem 1 except with N = 8, find the value (at time) of an American call option with X = 100. Use the table below to evaluate (3,8,), the cdf of the binomial distribution with parameters N = 8, and p = y. Hint: To find m, because N is rather small, you should be able to quickly plug in values to determine when 100 * (1.2)*(.9)- > 100 0(,8,y) 2 = 1 X = 2 = 3 1 = 4 1 = 5 y = 0.4 0.106 0.315 0.594 0.826 0.95 y = 0.47 0.05 0.187 0.429 0.7 0.89 y = 0.54 0.021 0.098 0.28 0.546 0.8 20 20 20 20 20 1. Consider a binomial model with N = 3 and: 0.2 : W. = u K(n) = -0.1 :wn=d and P(u) = p = 0.6 and S(0) = 100. (a) Write out the binomial tree showing S(n) for n = 0, 1, 2, 3. (b) Calculate the expected return from n = 0 to n = 3. (c) A long forward contract is entered at time 0. If the risk-free rate over a single time step in R=0.02, calculate the value of the forward contract at time n = 1 if you are in state u. Hint: B(n, N) = (1 + R)-(N-) 4. Use the Cox Ross Rubinstein formula and the binomial model described in problem 1 except with N = 8, find the value (at time) of an American call option with X = 100. Use the table below to evaluate (3,8,), the cdf of the binomial distribution with parameters N = 8, and p = y. Hint: To find m, because N is rather small, you should be able to quickly plug in values to determine when 100 * (1.2)*(.9)- > 100 0(,8,y) 2 = 1 X = 2 = 3 1 = 4 1 = 5 y = 0.4 0.106 0.315 0.594 0.826 0.95 y = 0.47 0.05 0.187 0.429 0.7 0.89 y = 0.54 0.021 0.098 0.28 0.546 0.8 20 20 20 20 20 1. Consider a binomial model with N = 3 and: 0.2 : W. = u K(n) = -0.1 :wn=d and P(u) = p = 0.6 and S(0) = 100. (a) Write out the binomial tree showing S(n) for n = 0, 1, 2, 3. (b) Calculate the expected return from n = 0 to n = 3. (c) A long forward contract is entered at time 0. If the risk-free rate over a single time step in R=0.02, calculate the value of the forward contract at time n = 1 if you are in state u. Hint: B(n, N) = (1 + R)-(N-)