Question

Data: S₀ = 100; X = 120; 1 + r = 1.12. The two possibilities for S_T are 160 and 80.

a.	The range of S is 80 while that of P is 40 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.)

Hedge ratio

b-1.	Form a portfolio of one shares of stock and two 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

$

c.	Given that the stock currently is selling at $100, calculate the put value. (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Put value

$

Answer 1

a. Hedge Ratio = [P₍₊₎ - P_(-)]/[S₍₊₎ - S_(-)] = [MAX(120-160)-MAX(120-80)]/[160-80] = (0-40)/80 = -0.5

b1. 1 share & 2 stocks (will be delta neutral hedged portfolio).

At end of period,

if S_T = S₍₊₎ = 160, Portfolio value V_T = S₍₊₎ + 2*MAX(120- S₍₊₎,0) = 160 + MAX(120-160,0) = 160+0 = 160

if S_T = S_(-) = 80, Portfolio value V_T = S_(-) + 2*MAX(120- S_(-),0) = 80 + 2*MAX(120-80,0) = 80+2*40 = 160

Hence (nonrandom) payoff to this portfolio = $160.

b2. PV(Portfolio) = 160/1.12 = 142.8571429 = $ 142.86.

c. PV(Portfolio) = 142.8571429 = S₀ + 2*P₀ ...(1)

Substituting S₀=100 in (1), we get,

142.8571429 = 100 + 2*P₀

implies, P₀ = 42.8571429/2

implies P₀ = 21.42857145 = $ 21.43 .