Question

# Calculate the price of a European call option using the Black Scholes model and the following...

Calculate the price of a European call option using the Black Scholes model and the following data: stock price = \$56.80, exercise price = \$55, time to expiration = 15 days, risk-free rate = 2.5%, standard deviation = 22%, dividend yield = 8%.

 As per Black Scholes Model Value of call option = S*N(d1)-N(d2)*K*e^(-r*t) Where S = Current price = 56.8 t = time to expiry = 0.041666667 K = Strike price = 55 r = Risk free rate = 2.5% q = Dividend Yield = 8% σ = Std dev = 22% d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2) d1 = (ln(56.8/55)+(0.025-0.08+0.22^2/2)*0.0416666666666667)/(0.22*0.0416666666666667^(1/2)) d1 = 0.688525 d2 = d1-σ*t^(1/2) d2 =0.688525-0.22*0.0416666666666667^(1/2) d2 = 0.643618 N(d1) = Cumulative standard normal dist. of d1 N(d1) =0.754439 N(d1) = Cumulative standard normal dist. of d2 N(d2) =0.740088 Value of call= 56.8*0.754439-0.740088*55*e^(-0.025*0.0416666666666667) Value of call= 2.19

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