Question

1. Let's assume that we have a stock that is priced at $47 a share. There is a call that expires in 5 months that has a strike price of $44.50. The stock has a standard deviation of .35 and the risk free rate is 2.25%.

   Let's find the price of this call using the BSOPM.

   What is the N of d₂?

   	A.	.3688
   	B.	.6541
   	C.	.2731
   	D.	.5677

Answer 1

As per Black Scholes Model
Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		47
t = time to expiry =		0.416667
K = Strike price =		44.5
r = Risk free rate =		2.3%
q = Dividend Yield =		0%
σ = Std dev =		35%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(47/44.5)+(0.0225-0+0.35^2/2)*0.416667)/(0.35*0.416667^(1/2))
d1 = 0.396391
d2 = d1-σ*t^(1/2)
d2 =0.396391-0.35*0.416667^(1/2)
d2 = 0.170467
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.654092
N(d2) = Cumulative standard normal dist. of d2
N(d2) =0.5677