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.)

(Do not round intermediate calculations. Round your answer to 2 decimal places.)

Explanation / Answer

Answer:First step is to make the stockís payoff diffference in the two states is the same as the call. We can achieve that by buying only half a share.

=-70/4=-17.5

=85/4=21.25

40/4=10

Then, we must add some borrowing at interest rate1 +r= 1:09. The goal is to make the payoff to become zero in the bad state.

=10/1.09=9.17

Add the stock holding and the borrowing to see

=-17.5+9.17=-8.33

The payoff is the same as the call option. Therefore,

-C=-8.33 or C=8.33

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