Question

You are attempting to value a call option with an exercise price of $65 and one year to expiration. The underlying stock pays no dividends, its current price is $65, and you believe it has a 50% chance of increasing to $90 and a 50% chance of decreasing to $40. 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.

Answer 1

In 1 year when Stock price rises to 90 then call option = Expected price - Exercise price =90 -65 =25
When stock price is 40 then call option = 0 ( When stock price is less than call price then call option value =0

The call option after 1 year =Probability of Increase in price * Call Option when price rises + Probability of price fall* Call option when price falls =50%*25+50%*0 =12.50

Call option value today = 12.50/(1+risk free Rate) =12.50/(1+8%) =11.57