Question

Consider a stock selling for $100, with volatility (standard deviation) of 30% per year. The stock pays no dividends. The risk-free continuously compounded interest rate is 4%. What is the Black-Scholes value of a call option on this stock with strike price 95 and 3-month maturity?

Answer 1

In this case, S0 = 100; X = 95; r = 0.04; sd = 0.30 and T = 3/12

d1 = [{ln(S0/X)} + {t(r - q + sd²/2)}] / [sd(t)^1/2]

= [{ln(100/95)} + {(3/12)(0.04 + 0.30²/2)}] / [0.30(3/12)^1/2]

= 0.0725 / 0.15 = 0.483621963

d2 = d1 - [sd(t)^1/2]

= 0.4836 - [0.30(3/12)^1/2]

= 0.4836 - 0.15 = 0.3336

C = [S0 * e^-qt * N(d1)] - [X * e^-rt * N(d2)]

= [$100 * e^-0*(3/12) * N(0.4836)] - [$95 * e^-0.04*(3/12) * N(0.3336)]

= [$100 * 1 * 0.6857] - [$95 * 0.9901 * 0.6307]

= $68.57 - $59.32 = $9.25