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
UR  - http://www.nber.org/papers/w10579
L1  - http://www.nber.org/papers/w10579.pdf
N1  - Author contact info:
Yacine Ait-Sahalia
Department of Economics
Fisher Hall
Princeton University
Princeton, NJ 08544-1021
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  -