option with an exercise price of $109 and one year to expiration. The underlying stock pays no dividends, its current price is $109, and you believe it has a 50% chance of increasing to $131 and a 50% chance of decreasing to $87. The risk-free rate of interest is 8%. Calculate the call option's value using the two-state stock price model

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Business

Kaden Mcdonald

28 May, 17:19

option with an exercise price of $109 and one year to expiration. The underlying stock pays no dividends, its current price is $109, and you believe it has a 50% chance of increasing to $131 and a 50% chance of decreasing to $87. The risk-free rate of interest is 8%. Calculate the call option's value using the two-state stock price model

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Cael Salazar · Answer 1

The value of the call option today is $10.19

Explanation:

The value of the call option under the two state stock price model is calculated by calculating the present value of the expected return on the stock based on the price increase and price decrease and the probability of such change in prices. It assumes the price to be such that the price is arbitrage free price.

The return on stock is 131 - 109 = 22 if the prices rise to $131. The option will be exercised in this case.

The return on stock will be 0 in case prices go down to $87 as the option will not be exercised and it will expire worthless.

The expected return is = 22 * 0.5 + 0 * 0.5 = $11

The present value of the return is 11 / (1+0.08) = $10.185 rounded off to $10.19

Thus, the price of the call option today is $10.19