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?
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
Consider a stock selling for $100, with volatility (standard deviation) of 30% per year. The stock...
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?
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