Question

What is the price of a European call option on a non-dividend-paying stock when
the stock price is $52, the strike price is $50, the risk-free interest rate is 12% per annum, the
volatility is 30% per annum, and the time to maturity is three months? (Hint: Remember Black-
Sholes-Merton Model. Please refer to the N(d) tables provided to you to pick the N values you
need)

Answer 1

So = 52

K - 50

r = 0.12

rho = 30

T = 0.25

d1 = [ln(52/50) + (0.12+0.3^2/2)*0.25]/(0.3 * sqrt(0.25))

= 0.5365

d2 = d1 - 0.3*sqrt(0.25)

= 0.3865

price of european call

= 52 * N(0.5365) - 50 * e^(-0.23*0.25) * N(0.3865)

= 52 * 0.7042 - 50 * e^-0.03 * 0.6504

= 5.06

So = 52

K - 50

r = 0.12

rho = 30

T = 0.25

d1 = [ln(52/50) + (0.12+0.3^2/2)*0.25]/(0.3 * sqrt(0.25))

= 0.5365

d2 = d1 - 0.3*sqrt(0.25)

= 0.3865

price of european call

= 52 * N(0.5365) - 50 * e^(-0.23*0.25) * N(0.3865)

= 52 * 0.7042 - 50 * e^-0.03 * 0.6504

= 5.06