Question

15: Interest rates are 10% per annum continuously compounded. The price of the stock is currently $100 per share. In one year the price will be either $125 per share or $75 per share. Using a one period Binomial Tree Model as outlined in Section 75, find the value, now, of the call option with exercise price of 100. What is the hedge ratio? Now calculate the answers for exercise prices of 90 and 110.

Answer 1

a). The two possible stock prices are:

S+ = $125 and S– = $75. Therefore, since the exercise price is $100, the corresponding two possible call values are:

Cu= $125 - $100 = $25 and Cd= $75 - $100 = $0

Hedge Ratio = (Cu– Cd)/(uS0– dS0) = (25 – 0)/(125 – 75) = 25/50 = 0.5

b). Since the exercise price is $90, the corresponding two possible call values are:

Cu= $125 - $90 = $35 and Cd= $75 - $90 = $0.

Hedge Ratio = (Cu– Cd)/(uS0– dS0) = (35 – 0)/(125 – 75) = 35/50 = 0.7

c). Since the exercise price is $110, the corresponding two possible call values are:

Cu= $125 - $110 = $15 and Cd= $75 - $110 = $0.

Hedge Ratio = (Cu– Cd)/(uS0– dS0) = (15 – 0)/(125 – 75) = 15/50 = 0.3