Question

# Let S = \$100, K = \$120, σ = 30%, r = 0.08, and δ =...

Let S = \$100, K = \$120, σ = 30%, r = 0.08, and δ = 0. Compute the Black-Scholes call price for 1 year to maturity.

 As per Black Scholes Model Value of call option = S*N(d1)-N(d2)*K*e^(-r*t) Where S = Current price = 100 t = time to expiry = 1 K = Strike price = 120 r = Risk free rate = 8.0% q = Dividend Yield = 0% σ = Std dev = 30% d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2) d1 = (ln(100/120)+(0.08-0+0.3^2/2)*1)/(0.3*1^(1/2)) d1 = -0.191072 d2 = d1-σ*t^(1/2) d2 =-0.191072-0.3*1^(1/2) d2 = -0.491072 N(d1) = Cumulative standard normal dist. of d1 N(d1) =0.424235 N(d1) = Cumulative standard normal dist. of d2 N(d2) =0.311688 Value of call= 100*0.424235-0.311688*120*e^(-0.08*1) Value of call= 7.9

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