1a) Let S = $50, K = $55, r = 8% (continuously compounded), T = 0.25, and d = 0.

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?

D = –0.5055; B = 48.6981

D = –0.6640; B = 34.3515

D = –0.9695; B = 48.6535

D = –0.7273; B = 44.5545

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.

$9.491

$8.257

$7.023

$7.972

$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.)

u = 1.5537; d = 0.9108

u = 1.1509; d = 0.6546

u = 1.3034; d = 0.7859

u = 1.5836; d = 0.6012

u = 1.0610; d = 0.5556

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

Explanation / Answer

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

u = 1.3034; d = 0.7859

c.

u = 1.3034; d = 0.7859

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