Data. So = 107, X = 110; 1 + r = 1.12. The two possibilities for ST are 155 and

Question

Data. So = 107, X = 110; 1 + r = 1.12. The two possibilities for ST are 155 and 95. The range of S is 60 while that of P is 15 across the two states. What is the hedge ratio of the put? Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.) a. Hedge ratic b-1. Form a portolio of one shares of stock and four puts. What is the (nonrandom) payoff to this portfolio? (Omit the "$" sign in your response.) Nonrandom payoff b-2. What is the present value of the portfolio? (Round your answer to 2 decimal places. Omit the "$" sign in your response.) Present value Given that the stock currently is selling at $107, calculate the put value. (Round your answer to 2 c. decimal places. Omit the "$" sign in your response.) Put value

Explanation / Answer

S = 107, X = 110, Su = 155, Sd = 95

Put Payoff: Pu = 0, Pd = 110 - 95 = 15

R = 1 + r = 1.12

Risk-neutral probability: p = (R - d)/(u - d)

p = (1.12 - 95/107)/(155/107 - 95/107) = 0.4140

1 - p = 0.5860

a:

Hedge ratio = (Pu - Pd)/(Cu - Cd) = (0 - 15)/(155 - 95) = -15/60 = -0.25

b:

V = St + 4Pt

Payoff: Vu = 155, Vd = 95 + 4*15 = 155

Both are same; non-random payoff = 155

c:

PV = 155/1.12 = 138.39

d:

P = [p*Pu + (1 - p)*Pd]/R

p = (0.4140*0 + 0.5860*15)/1.12 = 7.85

Put value = $7.85

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