You are attempting to value a call option with an exercise price of $140 and one

Question

You are attempting to value a call option with an exercise price of $140 and one year to expiration. The underlying stock pays no dividends, its current price is $140, and you believe it has a 50% chance of increasing to $160 and a 50% chance of decreasing to $120. The risk-free rate of interest is 10%. Based upon your assumptions, calculate your estimate of the the call option's value using the two-state stock price model. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Value of the call            $

Explanation / Answer

Exercise price X = $140
Time to expiration T = 1 year
Current price of stock S0 = $140
Value of stock when price goes up uS0 = $160
Value of stock when price goes down dS0 = $120
Risk free interest rate rs = 10%
Calculate hedge ratio =
H = Cu - Cd / uS0 - dS0
Where, Cu = $160 - $140 = $20
Cd = 0
H = 20 / (160 - 120) = 0.50

Using the single period binomial model the value of call option at node B =
C = Cu*p - Cd *(1- p) / r
= (20 * 0.5 - 0 * 0.5) / 1.1
= 9.091
VAlue of option at node A =
= (9.091 * 0.5 + 0 * .5) / 1.1
= 4.13

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