You are attempting to value a call option with an exercise price of $70 and one

Question

You are attempting to value a call option with an exercise price of $70 and one year to expiration. The underlying stock pays no dividends, its current price is $70, and you believe it has a 50% chance of increasing to $85 and a 50% chance of decreasing to $40. The risk-free rate of interest is 9%. 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 = 70,

stock current price S0 = 70

risk-free rate r = 9%,

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

the stock price a year later

Su = 85 , Sd = 40

1.calculate u and d

u = Su/S0 = 85/70 = 1.214

d = Sd/S0 = 40/70 = 0.5714

2.calculate the call value at expiry date

Cu = max(Su - X , 0) = max(85 - 70 , 0) = 5

Cd = max(Sd - X , 0) = max(40 - 70 , 0) = 0

3.calculate the call value today

c0=[1+r-d/u-d]*(cu/1+r)+(u-1-r/u-d)*(cd/1+r)

=[1+0.09-0.5714/1.214-0.5714]*(5/1+0.09)+(1.214-1-0.09)*(0/1+0.09)

=[0.5186/0.6426]*4.59=$3.704 or 370.4%

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