Question

We will derive a two-state put option value in this problem. Data: So = 110; X = 120; 1 + r= 1.1. The two possibilities for Stare 140 and 100. a. The range of Sis 40 while that of Pis 20 across the two states. What is the hedge ratio of the put? (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) Hedge ratio b. Form a portfolio of 2 shares of stock and 4 puts. What is the (nonrandom) payoff to this portfolio? (Round your answer to 2 decimal places.) Nonrandom payoff

Answer 1

a). uS0 = 140; Pu = 0;

dS0 = 100; Pd = 110 - 100 = 10;

Hedge Ratio = [Pu - Pd] / [uS0 - dS0] = [0 - 10] / [140 - 100] = -10 / 40 = -1/4

b).

Riskless Portfolio	St = 100	St = 140
Buy 1 share	100	140
Buy 4 Puts	40	0
Total	140	140

c). Present Value = $140 / 1.1 = $127.27

d). Portfolio's Cost = 1S + 4P = 1($110) + 4P = $110 + 4P

Value of the Portfolio = $127.27

So,

$110 + 4P = $127.27

4P = $127.27 - $110

P = $17.27 / 4 = $4.32