7.095 is not the correct answer. Cannot seem to figure this one out. Please advi

Question

7.095 is not the correct answer. Cannot seem to figure this one out. Please advise

You are attempting to value a call option with an exercise price of S107 and 1 year to expiration. The underlying stock pays no dividends, its current price is $107, and you believe it has a 50% chance of increasing to $123 and a 50% chance of decreasing to S91. The risk-free rate of interest is 12%. Calculate the call option's value using the two-state stock price model. (Do not round intermediate calculations and round your final answer to 2 decimal places. Omit the "$" sign in your response.) Call option's value

Explanation / Answer

Call Option Calculate the option values at expiration. The two possible stock prices and the corresponding call values are: uS 0 = 123 C u = 16 dS 0 = 91 C d = 0 Calculate the hedge ratio H = C u - C d / uSo - d S o = 16 - 0 / 123 - 91 = 1/2 Therefore, form a riskless portfolio by buying one share of stock and writing two calls. The cost of the portfolio is: S – 2C = 107 – 2C Show that the payoff for the riskless portfolio equals $91 Riskless Portfolio S = 91 S = 123 Buy 1 share 91 123 Write 2 calls 0 -16 Total 91 91 Therefore, find the value of the call by solving: $107 – 2C = $91/1.12 C = $12.875 Notice that we did not use the probabilities of a stock price increase or decrease. These are not needed to value the call option.

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