Question

Reconsider the determination of the hedge ratio in the two-state model where we showed that one-third share of stock would hedge one option. The possible end-of-year stock prices, uS0 = $120 (up state) and dS0 = $80 (down state). a. What would be the call option hedge ratio for each of the following exercise prices: $120, $104, $93, $80, given the possible end-of-year stock prices, uS0 = $120 (up state) and dS0 = $80 (down state)?

Answer 1

Exercise prices (Hedge ratio): $120 (0.000), $104 (0.400), $93 (0.675), $80 (1.000).

Step-by-step explanation:

Upper state (uS0) = 120

Down State (dS0) = 80

Difference = 40

Exercise Price($) Hedge Ratio

120 120-120/40 = 0/40 = 0.000

104 120-104/40 = 16/40 = 0.400

93 120-93 = 27/40 = 0.675

80 120-80/40 = 40/40 = 1.000

As the option becomes more in the money, the hedge ratio increases to a maximum of 1.0.