Question

Suppose a stock is currently trading at 92 and the annual risk free rate is 0.0018.

What is the price of a call option on this stock with an expiration date T = 0.5 (times in years) and with an exercise price K = 98. Assume the volatility of annual log return is sd = 0.2

What is the price of a put option on the same stock with the same parameters

Answer 1

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		92
t = time to expiry =		0.5
K = Strike price =		98
r = Risk free rate =		0.2%
q = Dividend Yield =		0%
σ = Std dev =		20%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(92/98)+(0.0018-0+0.2^2/2)*0.5)/(0.2*0.5^(1/2))
d1 = -0.369668
d2 = d1-σ*t^(1/2)
d2 =-0.369668-0.2*0.5^(1/2)
d2 = -0.511089
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.355815
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.304644
Value of call= 92*0.355815-0.304644*98*e^(-0.0018*0.5)
Value of call= 2.91

As per Black Scholes Model
Value of put option = N(-d2)*K*e^(-r*t)-(S)*N(-d1)
Where
S = Current price =		92
t = time to expiry =		0.5
K = Strike price =		98
r = Risk free rate =		0.2%
q = Dividend Yield =		0%
σ = Std dev =		20%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(92/98)+(0.0018-0+0.2^2/2)*0.5)/(0.2*0.5^(1/2))
d1 = -0.369668
d2 = d1-σ*t^(1/2)
d2 =-0.369668-0.2*0.5^(1/2)
d2 = -0.511089
N(-d1) = Cumulative standard normal dist. of -d1
N(-d1) =0.644185
N(-d2) = Cumulative standard normal dist. of -d2
N(-d2) =0.695356
Value of put= 0.695356*98*e^(-0.0018*0.5)-92*0.644185
Value of put= 8.82