We will derive a two-state put option value in this problem. Data: S 0 = 280; X

Question

We will derive a two-state put option value in this problem. Data: S0 = 280; X = 290; 1 + r = 1.1. The two possibilities for ST are 320 and 200.

The range of S is 120 while that of P is 90 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.)

Form a portfolio of 3 shares of stock and 4 puts. What is the (nonrandom) payoff to this portfolio?(Round your answer to 2 decimal places.)

Given that the stock currently is selling at 280, calculate the put value. (Round your answer to 2 decimal places.)

We will derive a two-state put option value in this problem. Data: S0 = 280; X = 290; 1 + r = 1.1. The two possibilities for ST are 320 and 200.

Explanation / Answer

Solution:

Hedge ratio = Cu - Cd /uSo-dSo

=Cu = 290 - 320 = 0

Cd = 290 -200 = 90

= 0 - 90 /320-200 = -.75

if price of share decrease by $1 then the price of the put will decrease by .75

Particulars                                  CAll    320                             Put   200

buy 3    calls                                        960                                      600

buy 4 puts                                             0                           4*90 = 360

total 960     960

Hence the present value = 960/1.1 = 872.73

In equilibrium put value = 3* 280 + 4P = 872.73

= 840 + 4 P = 872.73

Put value P = 32.73/4

= $8.1825
       

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