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Answer :
Final answer:
The hedge ratio of the call is 0.2. The value of the call option is $2.
Explanation:
a-1. Hedge Ratio of the Call:
The hedge ratio of a call option can be calculated using the formula:
Hedge Ratio = Change in Option Price / Change in Underlying Asset Price
In this case, the range of S is 50, while the range of C is 10 across the two states. The change in option price is 10, and the change in underlying asset price is 50. Therefore, the hedge ratio of the call is:
Hedge Ratio = 10 / 50 = 0.2
a-2. Value of the Call Option:
To calculate the value of a call option in a two-state model, we need to consider the probabilities of the two possible states and their corresponding payoffs.
Given that the two possibilities for ST are 130 and 80, we can calculate the probabilities of each state:
Probability of ST = 130: (1 + r - ST) / (ST - X) = (1 + 1.2 - 130) / (130 - 120) = 0.2
Probability of ST = 80: (1 + r - ST) / (ST - X) = (1 + 1.2 - 80) / (80 - 120) = 0.8
Next, we calculate the payoffs in each state:
Payoff when ST = 130: ST - X = 130 - 120 = 10
Payoff when ST = 80: 0
Finally, we calculate the value of the call option:
Value of Call Option = (Probability of ST = 130 * Payoff when ST = 130) + (Probability of ST = 80 * Payoff when ST = 80)
Value of Call Option = (0.2 * 10) + (0.8 * 0) = 2
a-1. Hedge Ratio of the Call: 0.2
a-2. Value of the Call Option: $2
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