Question

Part II (Binomial Tree) ai' 1. Compute the price of a call option using the stock price tree u1.4634 and d=0.7317. The stock price is $38. The strike price is 840 and the interest rate is 8%. The time-period is 6 month. Use a 2 stage binomial tree 2. Assume that where ?-8%, the dividend yield ?. 0, ? is the annual standard deviation and ?VE is the standard deviation over a period of length h. The initial stock price is 341 . Here, sigma-30% and the maturity T:h a) Use the binomial tree to find the price of a 40 strike price call option with matutity T-1 b) Use the binomial tree to find the price of a 40 strike price call option with matutity T-2 c) Use the binomial tree to find the price of a 40 strike price call option with matutity T-3

Answer 1

1.

Two stage Binomial Tree: t = 1/2 = 0.5 n = 82 p. a i.e 42 p a every 6 month i.e R = 1.04 p = R - d/ U - d = 1.04 - 0.7317/1.4634 - 0.7317 = 0.3083/0.7317 = 0.42 1 - p = 0.58 Value of Cu = p Cuu + (l- p) Cud/R = 0.42 times 41.37 + (0.58) 0.68/1.04 = 17.09 Value of Cd = p Cud + (l- p) Cdd/R = 0.42 times 0.68 + 0.58 times 10/1.04 = 0.27 Value of all = p Cu + (l- p) Cul/R = 1.42 times 17.09+ (0.58) 0.27/1.04 = 7.06 When T = 2 u = e^(0.08 - 0)2 + 0.3 squareroot 2 = e^0.58 = 1.786 d = e^(0.08 - 0)2 - 0.3 squareroot 2 = e^0.26= 0.771 p = 1.08 - 0.771/1.786 - 0.771 = 0.309/1.015 = 0.3 l - p = 0.7 Cu = 0.3 times 86.59 + 0.7 times 14.05/1.08 = 33.18