Question

Consider a 1-year option with exercise price $100 on a stock with annual standard deviation 15%. The T-bill rate is 2% per year. Find N(d1) for stock prices (a) $95, (b) $100, and (c) $105. (Do not round intermediate calculations. Round your answers to 4 decimal places.)

S	N(d1)
$95
$100
$105

Answer 1

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		95
t = time to expiry =		1
K = Strike price =		100
r = Risk free rate =		2.0%
q = Dividend Yield =		0%
σ = Std dev =		15%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(95/100)+(0.02-0+0.15^2/2)*1)/(0.15*1^(1/2))
d1 = -0.133622
d2 = d1-σ*t^(1/2)
d2 =-0.133622-0.15*1^(1/2)
d2 = -0.283622
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.4469

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		100
t = time to expiry =		1
K = Strike price =		100
r = Risk free rate =		2.0%
q = Dividend Yield =		0%
σ = Std dev =		15%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(100/100)+(0.02-0+0.15^2/2)*1)/(0.15*1^(1/2))
d1 = 0.208333
d2 = d1-σ*t^(1/2)
d2 =0.208333-0.15*1^(1/2)
d2 = 0.058333
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.5825

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		105
t = time to expiry =		1
K = Strike price =		100
r = Risk free rate =		2.0%
q = Dividend Yield =		0%
σ = Std dev =		15%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(105/100)+(0.02-0+0.15^2/2)*1)/(0.15*1^(1/2))
d1 = 0.533601
d2 = d1-σ*t^(1/2)
d2 =0.533601-0.15*1^(1/2)
d2 = 0.383601
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.7032