TY - JOUR
AU - Ait-Sahalia,Yacine
AU - Kimmel,Robert
TI - Maximum Likelihood Estimation of Stochastic Volatility Models
JF - National Bureau of Economic Research Working Paper Series
VL - No. 10579
PY - 2004
Y2 - June 2004
DO - 10.3386/w10579
UR - http://www.nber.org/papers/w10579
L1 - http://www.nber.org/papers/w10579.pdf
N1 - Author contact info:
Yacine Aït-Sahalia
Department of Economics
Bendheim Center for Finance
Princeton University
Princeton, NJ 08540
Tel: 609/258-4015
Fax: 609/258-0719
E-Mail: yacine@princeton.edu
Robert Kimmel
Ohio State University
E-Mail: kimmel_42@cob.osu.edu
AB - 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.
ER -