Question

1.         What is the value of the following call option according to the Black Scholes Option Pricing Model? What is the value of the put options?

                                               Stock Price = $42.50

                                               Strike Price = $45.00

                                               Time to Expiration = 3 Months = 0.25 years.

                                               Risk-Free Rate = 3.0%.

                                               Stock Return Standard Deviation = 0.45.

Answer 1

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		42.5
t = time to expiry =		0.25
K = Strike price =		45
r = Risk free rate =		3.0%
q = Dividend Yield =		0%
σ = Std dev =		45%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(42.5/45)+(0.03-0+0.45^2/2)*0.25)/(0.45*0.25^(1/2))
d1 = -0.108204
d2 = d1-σ*t^(1/2)
d2 =-0.108204-0.45*0.25^(1/2)
d2 = -0.333204
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.456917
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.36949
Value of call= 42.5*0.456917-0.36949*45*e^(-0.03*0.25)
Value of call= 2.92

As per Black Scholes Model
Value of put option = N(-d2)*K*e^(-r*t)-(S)*N(-d1)
Where
S = Current price =		42.5
t = time to expiry =		0.25
K = Strike price =		45
r = Risk free rate =		3.0%
q = Dividend Yield =		0%
σ = Std dev =		45%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(42.5/45)+(0.03-0+0.45^2/2)*0.25)/(0.45*0.25^(1/2))
d1 = -0.108204
d2 = d1-σ*t^(1/2)
d2 =-0.108204-0.45*0.25^(1/2)
d2 = -0.333204
N(-d1) = Cumulative standard normal dist. of -d1
N(-d1) =0.543083
N(-d2) = Cumulative standard normal dist. of -d2
N(-d2) =0.63051
Value of put= 0.63051*45*e^(-0.03*0.25)-42.5*0.543083
Value of put= 5.08