Maximum Likelihood Estimation of Stochastic Volatility Models
NBER Working Paper No. 10579
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.
Published: Ait-Sahalia, Yacine and Robert Kimmel. "Maximum Likelihood Estimation of Stochastic Volatility Models." Journal of Financial Economics 83, 2 (February 2007): 413-52.