Question

^{_{Find the price of an American call option on a futures if the current spot price is 30, the exercise price is 25, the futures price is 33.70, the risk-free interest rate is 6 percent, the spot asset can go up by 10 percent or down by 8 percent per period and the call expires in two periods, which is also when the futures expires.}}

Answer 1

Given ey It is a call option where anderlying asset is futures enercise price (X) = 25 spot price (sp) - 30 Risk free interest rate - CR - 6% pia call foupires in a Pentada Caleala bow here number of months of years in a a period is not given therefore we assume period = 1 yecey. Yearlo Yeout 22 +10E- 3637 Чес 12 tot 13B - 8.5. Box +10% 30.36 € -84) (27.6% +108_3036) -8.) 25.39G computation of probabiory of Increase in Spot paire probability of Higher price = Rad und where R = d = u= It Periodic i t. of 1 t t. of Interest rate Decrease Increase. dagen y = [17 05 06w] - [1 -0.08] (1+0.1) -(1-0008]

1.06 - 0.92 1.1 - 0.92 - 0.18 0.999 77.78% te poobability of lower spot proc probability of e sa Higher Sporpoice |- 77.784 22-22) - = for payoff & Binomad free Yeauro option value. ܙܩ@ge Secuz 72.98 . 39.98.). 9.438 D 12.281 28.22 1 7 11:3 22:22-3, 6:36] 74.88% 75.36F 22:224 0.39/G 22-22- 72.284 14.02 The above tree explanned below pagott @ Node Pos C . It is a call option option can be exercise only if market price exceeds 8000 exercise price

call payoff = sex m-x memoulet me 00 X Exercise price en [asis Diagram 1] payok @ NODE DE 36.3-25 - 11.3 @ Node € = 30-36-25 - 5.36 Node F = 30.36 -25 25-36 Node G = 25.39-25 - 0:39 Nalue @ Node B Higher of O payoff @ Node B 33-25 Discounted value of espected payolls @ Node DDE le 11.3 x 72.78] + 6-36 x 2924 1 +0.06 8.79+ 1.19 = 9.42 mo a value Node B= 9.42

value @ Nodec on Higher of o payoll @ Node c. 276-25 = 2.6 Discounted value of expected payol, 30 Node F&G le (5-36 x 77.78%] + 10.39% 22.227 1.06 6 os.ro 4.17 +0:09 pro 1.06 = 4:02 value@ Node c = 4,02 Value @ Node A Discounted value of Expected payoff @ Node BPC [9:42 * 77.78%] + [4:02 x ad.22 %) 1+0.06 = 7,33 + 0.89 = 776 Therefore an American call option value of CPolice = 7.76