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. A. 9.98 B. 8.70 C. 7.73 D. 8.22 E. none of the above please show working out

Answer 1

ANSWER = C) 7.73

The probability of price increase =

P =( r - d )/ (u - d)

= (1.06 - 0.92) / (1.1 - 0.92)

= 0.7778

Therefore the p of price decrease = 1 - 0.7778 = 0.2222

The two step binomial tree

		D 36.30 (33 * 1.1)
	B 33 (30 * 1.10)
A (30)		E 30.36 (33*0.92)/(27.60*1.1)
	C 27.60 (30 * 0.92)
		F 25.392 (27.60 * 0.92)

Value of option at Node B

C = Cu P - Cd (1- P) / R

= (11.30 * 0.7778 + 5.36 * 0.2222 ) /1.06

= 9.415

Value of option at Node C

C = Cu P - Cd (1- P) / R

= (5.36 * 0.7778 + 0.392 * 0.2222 ) /1.06

= 4.01

Value at node A = (9.415 * 0.7778 + 4.01 * 0.2222 ) / 1.06

= 7.73