A stock is currently selling for $56 a share.The risk-free rate is 3 percent and the standard deviation is 18 percent.What is the value of d1 of a 9-month call option with a strike price of $57.50?
A)-0.01506
B)0.05271
C)0.05740
D)0.06420
E)0.06752

Question

Quizplus · Accepted Answer

The value of d1 in the Black-Scholes model is calculated using the formula: $d1 = \frac{\ln(\frac{S}{K}) + (r + \frac{\sigma^2}{2})T}{\sigma\sqrt{T}}$, 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: $S = 56$, $K = 57.5$, $r = 0.03$, $\sigma = 0.18$, and $T = \frac{9}{12}$ (since 9 months is 3/4 of a year), we calculate d1. The correct calculation leads to the value closest to 0.05271, making option B the correct answer.

A Stock Is Currently Selling for $56 a Share