Question

a. Consider a call option. If, in a two-state model, a stock can take a price of $176 or $132, what would be the hedge ratio for each of the following exercise prices: $176, $170, $160, $132? (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.)

X		Hedge Ratio
$	176
$	170
$	160
$	132

b. What do you conclude about the hedge ratio as the option becomes progressively more in the money?

	Increases to a maximum of 1.0
	Decreases to a minimum of 0

Answer 1

a). The two possible stock prices are:

S+ = $176 and S– = $132.

If X = $176

Cu = $0 and Cd= $0.

Hedge Ratio = (Cu– Cd)/(uS0 – dS0) = (0 – 0)/(176 – 132) = 0/44 = 0

If X = $170

Cu = $6 and Cd= $0.

Hedge Ratio = (Cu– Cd)/(uS0 – dS0) = (6 – 0)/(176 – 132) = 6/44 = 0.14

If X = $160

Cu = $16 and Cd= $0.

Hedge Ratio = (Cu– Cd)/(uS0 – dS0) = (16 – 0)/(176 – 132) = 16/44 = 0.36

If X = $132

Cu = $44 and Cd= $0.

Hedge Ratio = (Cu– Cd)/(uS0 – dS0) = (44 – 0)/(176 – 132) = 44/44 = 1

b). As the option becomes progressively more in the money, its hedge ratio increases.