Question

1a)

Let S = $50, K = $55, r = 8% (continuously compounded), T = 0.25, and d = 0. Let u = 1.25, d = 0.7, and n = 1. What are D and B for a European put?

Answers:	a. D = –0.5055; B = 48.6981
	b. D = –0.6640; B = 34.3515
	c. D = –0.9695; B = 48.6535
	d. D = –0.7273; B = 44.5545
	e. D = –0.5607; B = 48.2080

1b) Let S = $65, K = $70, r = 3% (continuously compounded), T = 1, and d = 0. Let u = 1.25, d = 0.7, and n = 1. Calculate the value of a European put if D = –0.685315 and B = 54.0362.

Answers:	a. $9.491
	b. $8.257
	c. $7.023
	d. $7.972
	e. $11.768

1c)

Let S = $40, K = $35, r = 7% (continuously compounded), d = 4%, s = 40%, and T = 2. What are the appropriate values of u and d to build a 5-period binomial stock price tree? (Use the formulas from the main part of the chapter and lecture notes, not the alternative formulas in the appendix.)

Answers:	a. u = 1.5537; d = 0.9108
	b. u = 1.1509; d = 0.6546
	c. u = 1.3034; d = 0.7859
	d. u = 1.5836; d = 0.6012
	e. u = 1.0610; d = 0.5556

Answer 1

1a)

Su = 1.25*50 = 62.5

Sd = 0.7*50 = 35

Pu = 0

Pd = 55 - 35 = 20

D = (Pu -Pd)/(u-d)S = -20/(0.55*50) = - 0.7273

B = (u*Pd - d*Pu)*e^(-rt)/(u-d) = (1.25*20 - 0.7*0)*e^(-0.08*0.25)/(1.25-0.7) = 44.54

Ans is d. D = –0.7273; B = 44.5545

1b) Let S = $65, K = $70, r = 3% (continuously compounded), T = 1, and d = 0. Let u = 1.25, d = 0.7, and n = 1. Calculate the value of a European put if D = –0.685315 and B = 54.0362.

P = D*S + B = -0.685315*65 + 54.0362 = $9.49

Ans is a. $9.491

1c) Let S = $40, K = $35, r = 7% (continuously compounded), d = 4%, s = 40%, and T = 2. What are the appropriate values of u and d to build a 5-period binomial stock price tree? (Use the formulas from the main part of the chapter and lecture notes, not the alternative formulas in the appendix.)

Ans is

c. u = 1.3034; d = 0.7859