The GARCH process for stock prices has been used to better fit option prices. Which of the following best describes why GARCH may be used to fit the options smile?
A) GARCH is just one form of a stochastic volatility process and therefore random volatility causes the smile in the same way as does stochastic volatility.
B) GARCH implies persistence in changes in volatility, which in turn usually makes the return distribution have non-zero skewness and kurtosis.
C) GARCH volatility is deterministic and therefore causes the smile with certainty.
D) None of the above.

Question

Quizplus · Accepted Answer

GARCH implies persistence in changes in volatility, which can lead to non-zero skewness and kurtosis in the return distribution. This can better fit the observed options smile, where implied volatilities for out-of-the-money options are higher than for at-the-money options. Option prices are sensitive to changes in volatility, and incorporating this feature of volatility is important for accurately pricing options. Option prices also reflect the market's expectation for future volatility, and the persistence in volatility changes implied by GARCH can capture this expectation.

The GARCH Process for Stock Prices Has Been Used to Better