Question

A stock price is currently $40. It is known that at the end of one month that the stock price will either increase or decrease by 9%. The risk-free interest rate is 9% per annum with continuous compounding. What is the value of a one-month European call option with a strike price of $40? Equations you may find helpful: p = (e^(rΔt)-d) / (u-d) f = e^(-rΔt) * (fu*p + fd*(1-p)) (required precision 0.01 +/- 0.01)

Answer 1

Current Market price Down Price Up Price Exercise Price p = 40 36.4 43.6 40 Probability eart =2.7183^0.09*1/12 =down price/current price =up price / current price d = u = 1.01 0.910 1.090 p=r-d/u-d =1.0075-0.91/1.09-0.91 =0.5418 -0.5418 43.6 Cu= payoff = 43.6-40=3.6 36.4 Cd=0 Cu = Payoff if option exercise Cd = Payoff if option is not exercise

Value of call option =(Cu*p)+Cd*(1-P)/R = (3.6*0.5418)+0 *(1-0.5418)/1.03 = 1.89