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Journal of Financial Economics 83 (2007) 413452 Maximum likelihood estimation of stochastic

Summary: Journal of Financial Economics 83 (2007) 413ş452
Maximum likelihood estimation of stochastic
volatility models$
Yacine AiĘt-Sahalia├, Robert Kimmel
Department of Economics and Bendheim Center for Finance, Princeton University, Princeton, NJ, 08540, USA
Received 8 June 2004; received in revised form 23 September 2005; accepted 10 October 2005
Available online 11 September 2006
We develop and implement a 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 proxies based on the implied volatility of a short-
dated at-the-money option. The approximation results in a small loss of accuracy relative to the
standard errors due to sampling noise. 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 Heston model and a GARCH model,
suggests that the elasticity of variance of volatility lies between that assumed by the two nested
r 2006 Elsevier B.V. All rights reserved.
JEL classifications: G12; C22


Source: A´t-Sahalia, Yacine - Program in Applied and Comptutational Mathematics & Department of Economics, Princeton University


Collections: Mathematics