You are attempting to value a call option with an exercise price of $95 and one

Question

You are attempting to value a call option with an exercise price of $95 and one year to expiration. The underlying stock pays no dividends, its current price is $95, and you believe it has a 50% chance of increasing to $120 and a 50% chance of decreasing to $70. The risk-free rate of interest is 8%. 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

option exercise price X = 95

stock current price S0 = 95

risk-free rate r = 8%,

u = 1 + 50% = 1.5 , d = 1 - 50% = 0.5

the stock price a year later

Su = 120 , Sd = 70

1.calculate u and d

u = Su/S0 = 120/95 = 1.263158

d = Sd/S0 = 70/95 = 0.736842

2.calculate the call value at expiry date

Cu = max(Su - X , 0) = max(120 - 95 , 0) = 25

Cd = max(Sd - X , 0) = max(70 - 95 , 0) = 0

3.calculate the call value today

= ((1+8%- 0.736842)/(1.263158-0.736842))×(25/(1+8%))+((1.263158-1-8%)/(1.263158-0.736842))×(0/(1+8%))

= $39.35

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