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Answer :
Final answer:
The hedge ratio of the call is 0.8. The value of a call option on the stock with an exercise price of $100 is $18.18.
Explanation:
To calculate the hedge ratio of the call, we need to determine the number of shares of stock that need to be held for each call option. The hedge ratio is calculated as the change in the value of the call option divided by the change in the value of the stock. In this case, the range of the stock price (S) is $50, while the range of the call option price (C) is $40 across the two states.
The hedge ratio (H) can be calculated using the formula:
H = (C2 - C1) / (S2 - S1)
Substituting the given values:
H = ($40 - $0) / ($140 - $90) = $40 / $50 = 0.8
Therefore, the hedge ratio of the call is 0.8.
To calculate the value of a call option on the stock with an exercise price of $100, we can use the Black-Scholes formula or a binomial option pricing model. However, in this example, we are instructed not to use continuous compounding to calculate the present value of X, as the interest rate is quoted as an effective per-period rate.
Using the given data:
S0 = $120, X = $100, 1 + r = 1.10
We can calculate the value of the call option using the formula:
C = (S0 - X) / (1 + r)
Substituting the given values:
C = ($120 - $100) / (1.10) = $20 / 1.10 = $18.18
Therefore, the value of a call option on the stock with an exercise price of $100 is $18.18.
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