Question

You are attempting to value a call option with an exercise price of $100 and one year to expiration. The underlying stock pays no dividends, its current price is $100, and you believe it has a 50% chance of increasing to $130 and a 50% chance of decreasing to $70. The risk-free rate of interest is 10%. Calculate the call option's value using the two-state stock price model. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Answer:

$18.18

Explanation:

Calculation to determine the call option's value using the two-state stock price model

Based on the information given since the two possible stock prices are: S+ = $130 Increase and and S- = $70 decrease which means that If the exercise price is the amount of $100 the first step will be to determine the corresponding two possible call values.

First step is to determine the corresponding two possible call values.

Hence, the corresponding two possible call values are:

Cu = ($130-$100) and Cd = $0

Cu = $30 and Cd = $0

Second step is to Calculate the hedge ratio using this formula

Hedge ratio= (Cu - Cd)/(uS0 - dS0)

Hedge ratio= (30- 0)/(130 - 70)

Hedge ratio=30/60

Hedge ratio= 0.50

Third step is form the cost of the riskless portfolio and end-of-year value

Cost of the riskless portfolio = (S0 - 2C0)

Cost of the riskless portfolio = 100 - 2C0

End-of-year value =$70

Fourth step is to calculate the present value of $70 with a one-year interest rate of 10%:

Present value=$70/1.10

Present value= $63.64

Now let estimate the call option's value by first Setting the value of the hedged position to equal to the present value

Call option's value=$100 - 2C0 = $63.64

Hence,

C0=$100-$63.64/2

C0=$36.36/2

C0=$18.18

Therefore the call option's value using the two-state stock price model will be $18.18