A stock with a price of $72 has a dividend yield of 1 percent. There is a put option on the stock with a strike price of $75 that sells for $7.28 and has 49 days to maturity. If the risk-free rate is 5 percent, what is the implied standard deviation of the stock?
A) 48.27%
B) 55.06%
C) 42.86%
D) 30.15%
E) 37.29%

Question

Quizplus · Accepted Answer

The implied standard deviation, or implied volatility, of a stock can be calculated using the Black-Scholes model for pricing options. Given the information provided, the correct implied volatility is not directly calculable without using the Black-Scholes formula, which requires inputs such as the current stock price, the strike price of the option, the time to maturity (in years), the risk-free rate, and the price of the option. The correct answer (B) 55.06% is determined through the application of this model, indicating it is the result of a calculation specific to the given parameters.

A Stock with a Price of $72 Has a Dividend