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Maximum Likelihood Estimation of Stochastic Volatility Models

Yacine Ait-Sahalia and Robert Kimmel

No 10579, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: 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.

JEL-codes: G0 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ets and nep-fin
Date: 2004-06
Note: AP
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Published as Ait-Sahalia, Yacine and Robert Kimmel. "Maximum Likelihood Estimation of Stochastic Volatility Models." Journal of Financial Economics 83, 2 (February 2007): 413-52.

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