Maximum Likelihood Estimation of Stochastic Volatility Models / Yacine Ait-Sahalia, Robert Kimmel.

Format:

Book

Author/Creator:

Ait-Sahalia, Yacine.

Contributor:

National Bureau of Economic Research.

Kimmel, Robert.

Series:

Working Paper Series (National Bureau of Economic Research) no. w10579.

NBER working paper series no. w10579

Language:

English

Physical Description:

1 online resource: illustrations (black and white);

Place of Publication:

Cambridge, Mass. National Bureau of Economic Research 2004.

Summary:

We develop and implement a new method for maximum likelihood estimation in closed-form of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by the implied volatility of a short dated at-the-money option. We find that the approximation results in a negligible loss of accuracy. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine model of Heston (1993) and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.

Notes:

Print version record

June 2004.