Question

Stock price: $48

Exercise price : 46

Time to expiration: 1 year

Stock price variance: 0.40 per year

Risk-free interest rate (compounded continuously) 5% per year

A) at what price should a European call option with the above characteristics sell (Note: when calculating N(d1) and N(d2). please carry your estimates out to 4 digits

B) Is this call option in the money, at the money, or out of the money.

C) At what price should the corresponding put option sell?

Answer 1

Std dev = variance^(1/2) = 0.4^0.5=63.245%

A

As per Black Scholes Model
Value of call option = S*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		48
t = time to expiry =		1
K = Strike price =		46
r = Risk free rate =		5.0%
q = Dividend Yield =		0%
σ = Std dev =		63%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(48/46)+(0.05-0+0.63245^2/2)*1)/(0.63245*1^(1/2))
d1 = 0.462576
d2 = d1-σ*t^(1/2)
d2 =0.462576-0.63245*1^(1/2)
d2 = -0.169874
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.678166
N(d1) = Cumulative standard normal dist. of d2
N(d2) =0.432555
Value of call= 48*0.678166-0.432555*46*e^(-0.05*1)
Value of call= 13.62

B

Option is in the money as Stock price is more than exercise price

C

As per put call parity

Call price + PV of exercise price = Spot price + Put price

13.62+46/(1+0.05)^1=48+Put value

Put value = 9.43