Journal
JOURNAL OF FINANCIAL ECONOMICS
Volume 83, Issue 2, Pages 413-452Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.jfineco.2005.10.006
Keywords
closed-form likelihood expansions; volatility proxies; Heston model; GARCH model; CEV model
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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 models. (c) 2006 Elsevier B.V. All rights reserved.
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