Question

1a)

	Let S = $55, K = $50, r = 6% (continuously compounded), d = 2%, s = 40%, T = 0.5, and n = 5. In this situation, the appropriate values of u and d are 1.13939 and 0.88471, respectively. What is the value of p*, the risk-neutral probability of an upward movement in the stock price at any node of the binomial tree?
	Answers: a. 0.5316 b. 0.4998 c. 0.3738 d. 0.4146 e. 0.4684

1b)

	Let S = $65, r = 3% (continuously compounded), d = 5%, s = 30%, T = 2. In this situation, the appropriate values of u and d are 1.32313 and 0.72615, respectively. Using a 2-step binomial tree, calculate the value of a $55-strike European call option.
	Answers: a. $14.416 b. $14.291 c. $13.458 d. $13.868 e. $14.519

1c)

	Let S = $40, r = 5% (continuously compounded), d = 4%, s = 20%, T = 1.5. In this situation, the appropriate values of u and d are 1.19806 and 0.84730, respectively. Using a 2-step binomial tree, calculate the value of a $30-strike American call option.
	Answers: a. $10.327 b. $10.983 c. $10.579 d. $10.273 e. $10.190

1d)

	Suppose the exchange rate is $1.51/€. Let r$ = 6%, r€ = 7%, u = 1.34, d = 0.73, and T = 2. Using a 2-step binomial tree, calculate the value of a $1.45-strike European call option on the euro.
	Answers: a. $0.2425 b. $0.2361 c. $0.2151 d. $0.2284 e. $0.1960

1e)

	Suppose the exchange rate is $1.14/C$. Let r$ = 7%, rC$ = 4%, u = 1.33, d = 0.79, and T = 1.5. Using a 2-step binomial tree, calculate the value of a $1.20-strike American put option on the Canadian dollar.
	Answers: a. $0.1434 b. $0.1621 c. $0.1823 d. $0.1592 e. $0.1511

Answer 1

1a) Let S = $55, K = $50, r = 6% (continuously compounded), d = 2%, s = 40%, T = 0.5, and n = 5. In this situation, the appropriate values of u and d are 1.13939 and 0.88471, respectively. What is the value of p*, the risk-neutral probability of an upward movement in the stock price at any node of the binomial tree?

p = (e^rt - d) / (u-d) = (e^0.06*0.1 -0.88471)/(1.13939-0.88471) = 0.47

Ans is e) 0.4684

1b) Let S = $65, r = 3% (continuously compounded), d = 5%, s = 30%, T = 2. In this situation, the appropriate values of u and d are 1.32313 and 0.72615, respectively. Using a 2-step binomial tree, calculate the value of a $55-strike European call option.

Cuu = Suu - 55 = 65*1.32313*1.32313 - 55 = 58.7937

Cud = Sud - 55 = 65*1.32313*0.72615 - 55 = 7.45

Sdd = 65*0.72615*0.72615 = 34.274 < 55 ====> Cdd = 0

C = (58.79375*p^2 + 2*7.45*p*(1-p) + 0)*e^(-0.03*2)

p = (e^rT - d) / (u -d) = (e^(0.03*1) - 0.72615)/ (1.32313 - 0.72615) = 0.50974

C =

1c) Let S = $40, r = 5% (continuously compounded), d = 4%, s = 20%, T = 1.5. In this situation, the appropriate values of u and d are 1.19806 and 0.84730, respectively. Using a 2-step binomial tree, calculate the value of a $30-strike American call option

Su = 47.9224

Suu = 57.4139

Sd = 33.892

Sud = Sdu = 40.6046

Sdd = 28.71669

1d) Suppose the exchange rate is $1.51/€. Let r$ = 6%, r€ = 7%, u = 1.34, d = 0.73, and T = 2. Using a 2-step binomial tree, calculate the value of a $1.45-strike European call option on the euro

Euu = 1.51*1.34*1.34 - 1.45 = 2.711356 - 1.45 = 1.26

Eud = 1.51*1.34*0.73 - 1.45 = 0.027082

Edd = 0

p = (e^(0.06-0.07)-0.73)/(1.34-0.73) = 0.426

C = (p^2*Euu + 2*p*(1-p)*Eud)*e^(-0.06*2) = 0.2151

Ans is

c. $0.2151

1e) Suppose the exchange rate is $1.14/C$. Let r$ = 7%, rC$ = 4%, u = 1.33, d = 0.79, and T = 1.5. Using a 2-step binomial tree, calculate the value of a $1.20-strike American put option on the Canadian dollar.

Eu = 1.14*1.33 = 1.5162

Euu = 1.5162*1.33 = 2.016546

Eud = 1.14*1.33*0.79 = 1.197798

Ed = 1.14*0.79 = 0.9006

Edd = 0.711474

p = (e^(0.07 - 0.04)*1.5/2 - d ) /(u -d) = 0.431

at T= 1

Put option has value Pu = 1.188*10^-3 with p=0.431 & Pd = 0.2994 with pd=1-0.431

P = (0.4631*1.188*10^-3 + 0.537*0.299)*e^(-0.07*0.75) = 0.1621

Ans is b) 0.1621