Question

A stock price is currently $50. Over each of the next two three-month periods it is expected to go up by 7% or down by 6%. The risk-free interest rate is 9% per annum with continuous compounding. What is the value of a six-month European call option with a strike price of $49? 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

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Value of call option =(Cu*p)+Cd*(1-p)/R = (4.5*0.5194)+0 *(1-0.5194)/1.03 = 2.27

Current Market price Down Price Up Price Exercise Price 50 47 53.5 49 Probability eart =2.718310.09*1/12 =down price/current price =up price / current price p = r= d = 1.00753 0.940 1.070 p=r-d/u-d =1.0075-0.94/1.07-0.94 =0.5194 53.5 Cu= payoff = 53.5-49=4.5 =0.5194 50 47 Cd=0 Cu = Payoff if option exercise Cd = Payoff if option is not exercise

Value of call option =(Cu*p)+Cd*(1-p)/R = (4.5*0.5194)+0 *(1-0.5194)/1.03 = 2.27