Question

Calculate the Black and Scholes price of a European Call option, with a strike of $120 and a time to expiry of 6 months. The underlying currentely trades at $100 and has a (future) volatility of 23% p.a. Assume a risk free rate of 1% p.a. 0.07 0.08 O 1.20 O 1.24

Answer 1

S=100
E=120
t=6/12 =0.5 years
σ=23%
d1 =[ln(S/E) + (R – d + σ^2 / 2) × t] / (σ ×t^0.5) =(ln(100/120)+(1%-0+23%^2/2)*0.5)/(23%*0.5^0.5)=-1.00899
N(d1) =0.1565
d2=d1-σ*t^0.5 =-1.00899-23%*0.5^0.5 =-1.17162
N(d2) =0.12067
Call Price(C)= Stock Price * N(d1) – Exercise price × e–Rt × N(d2) =100*0.1565-120*EXP(-1%*0.5)*0.12067=1.24

(Option d is correct option)