Question

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%.

Answer #1

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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