Question

You are attempting to value a call option with an exercise price of $102 and one year to expiration. The underlying stock pays no dividends, its current price is $102, and you believe it has a 50% chance of increasing to $121 and a 50% chance of decreasing to $83. The risk-free rate of interest is 10%. Calculate the call option’s value using the two-state stock price model. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

If the stock ends up at $83, the call option expires worthless as the price at maturity is lower than the strike price

If the stock ends up at $121, the call option has a positive payoff of $19 (Stock price-strike price ie. $121-$102)

Both of these have equal probability of 0.5

For estimating the price of the call option, we discount the expected cash-flows at maturity by the risk-free rate

Call option's value = 0.5*0*e^(-0.1*1) + 0.5*19*e^(-0.1*1)

Call option's value = $8.60