Given that d1 = 1.50 in the Black-Scholes formula, the time to expiration of a call option is two months, the risk-free rate is 6% per year, and the standard deviation of returns on the shares
Underlying the call option is 20%. What is the value of d2 if the exercise price is $28 and the stock
Price is $31.23?
A) 1.42
B) 1.48
C) 1.50
D) 1.58

Question

Quizplus · Accepted Answer

Using the Black-Scholes formula:

d1 = [ln(S/X) + (r + (σ^2/2))(T)] / (σ√T)
d2 = d1 - σ√T

Where:
S = stock price
X = exercise price
r = risk-free rate
T = time to expiration (in years)
σ = standard deviation of returns

Plugging in the given values:

d1 = [ln(31.23/28) + (0.06 + (0.2^2/2))(2/12)] / (0.2√(2/12)) = 1.86
d2 = 1.86 - 0.2√(2/12) = 1.42

Therefore, the value of d2 is 1.42.

Given That D1 = 1