A stock is currently selling for $39 a share. The risk-free rate is 2.5 percent and the standard deviation is 26 percent. What is the value of d₁ of a 9-month call option with a strike price of $40?
A) −.01506
B) 0.08341
C) 0.07746
D) 0.06420
E) −.06752

Question

Quizplus · Accepted Answer

The value of $d_1$ in the Black-Scholes model is calculated using the formula: $$d_1 = \frac{\ln(\frac{S}{K}) + (r + \frac{\sigma^2}{2})T}{\sigma\sqrt{T}}$$ where $S$ is the current stock price, $K$ is the strike price, $r$ is the risk-free rate, $\sigma$ is the standard deviation of the stock's returns, and $T$ is the time to expiration in years. Plugging in the given values: $S = 39$, $K = 40$, $r = 0.025$, $\sigma = 0.26$, and $T = \frac{9}{12}$ (since 9 months is three-quarters of a year), we calculate $d_1$. The calculation yields a value that matches choice B, 0.08341, indicating it is the correct answer.

A Stock Is Currently Selling for $39 a Share