The volatility smile suggests that the Black-Scholes model underestimates the price of far-out-of-the-money options, as it assumes a lognormal distribution of stock prices which does not account for market skewness or kurtosis, leading to a smile-shaped curve when plotting implied volatilities against strike prices.

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The Volatility Smile

Question 28

Multiple Choice

The volatility smile

A) suggests that the prices for far-out-of-the-money options calculated using the Black-Scholes formula are lower than they are in reality.
B) is the result of plotting the Black-Scholes implied volatilities as a function of the stock price.
C) is the result of plotting the Black-Scholes strike prices as a function of the stock price.
D) suggests that prices for at-the-money options calculated using the Black-Scholes formula are higher than they are in reality.

Correct Answer: