Maximum likelihood estimation of stochastic volatility models

• 成果类型: Article
• 署名作者: Ait-Sahalia, Yacine; Kimmel, Robert
• 署名单位: Princeton University; Princeton University
• 刊物名称: JOURNAL OF FINANCIAL ECONOMICS
• ISSN/ISSBN: 0304-405X
• DOI: 10.1016/j.jfineco.2005.10.006
• 发表日期: 2007
• 页码: 413-452
• 关键词: closed-form likelihood expansions; volatility proxies; Heston model; GARCH MODEL; CEV model

摘要

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.