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ou are attempting to value a call 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 $142 and a 50% chance of decreasing to $76. The risk-free rate of interest is 12%. Calculate the call option's value using the two-state stock price model

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Answer:

$14.73

Explanation:

Given that, there is a 50 - 50 chance that a call option will either increase or decrease ;

Exercise price = $109

Increase price = $142

Decrease price = $76

Using the two state stock price model :

Increase price - exercise price ; 142 - 109 = $33

Decrease price - exercise price ; 76 - 109 - $33

We calculate the mean, expected value of winning after one year,

E(X) = Σx*p(x)

Since call won't be exercised if price decrease, then - 33 = 0

x : ___ 33 _____ 0

p(x) : _ 0.5 ____ 0.5

E(X) = (33*0.5) + (0*0.5)

E(X) = 16.5

The present value, PV = Expected winning / (1 + r)

PV = 16.5 / (1 + 0.12) = 16.5 / 1.12 = 14.73

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