Assume a stock price of $21.80, an exercise price of $20, three months to expiration, a risk-free rate of 3.40 percent, standard deviation of 46 percent, and a d₁ value of .52664. What is the value of d₂ as it is used in the Black-Scholes option pricing model?
A) .31218
B) .31225
C) .29664
D) .29535
E) .31340

Question

Quizplus · Accepted Answer

The value of $d_2$ in the Black-Scholes option pricing model can be calculated using the formula $d_2 = d_1 - \sigma\sqrt{T}$, where $\sigma$ is the standard deviation of the stock's returns, and $T$ is the time to expiration in years. Given $d_1 = 0.52664$, $\sigma = 0.46$, and $T = 3/12$ (since there are three months to expiration), we can calculate $d_2$ as follows: $d_2 = 0.52664 - 0.46\sqrt{3/12} = 0.52664 - 0.46\sqrt{0.25} = 0.52664 - 0.46 \times 0.5 = 0.52664 - 0.23 = 0.29664$.

Assume a Stock Price of $21