Estimating the leverage parameter of continuous-time stochastic volatility models using high frequency S&P 500 and VIX

Isao Ishida; Michael McAleer; Kosuke Oya

doi:10.1108/03074351111167938

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Managerial Finance

ISSN: 0307-4358

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Estimating the leverage parameter of continuous-time stochastic volatility models using high frequency S&P 500 and VIX

Document Information:
Title:	Estimating the leverage parameter of continuous-time stochastic volatility models using high frequency S&P 500 and VIX
Author(s):	Isao Ishida, (Center for the Study of Finance and Insurance, Osaka University, Osaka, Japan), Michael McAleer, (Erasmus School of Economics, Econometric Institute, Erasmus University Rotterdam, Rotterdam, The Netherlands, Tinbergen Institute, Rotterdam, The Netherlands, Institute of Economic Research, Kyoto University, Kyoto, Japan and Department of Quantitative Economics, Complutense University of Madrid, Madrid, Spain), Kosuke Oya, (Graduate School of Economics and Center for the Study of Finance and Insurance, Osaka University, Osaka, Japan)
Citation:	Isao Ishida, Michael McAleer, Kosuke Oya, (2011) "Estimating the leverage parameter of continuous-time stochastic volatility models using high frequency S&P 500 and VIX", Managerial Finance, Vol. 37 Iss: 11, pp.1048 - 1067
Keywords:	Continuous time, Gearing, High-frequency data, Implied volatility, S&P500, Stochastic volatility, Stock prices, VIX, Volatility
Article type:	Research paper
DOI:	10.1108/03074351111167938 (Permanent URL)
Publisher:	Emerald Group Publishing Limited
Acknowledgements:	JEL classification – G13, G17, G32
Abstract:	Purpose – The purpose of this paper is to propose a new method for estimating continuous-time stochastic volatility (SV) models for the S&P 500 stock index process using intraday high-frequency observations of both the S&P 500 index and the Chicago Board Options Exchange (CBOE) implied (or expected) volatility index (VIX). Design/methodology/approach – A primary purpose of the paper is to provide a framework for using intraday high-frequency data of both the indices' estimates, in particular, for improving the estimation accuracy of the leverage parameter, that is, the correlation between the two Brownian motions driving the diffusive components of the price process and its spot variance process, respectively. Findings – Finite sample simulation results show that the proposed estimator delivers more accurate estimates of the leverage parameter than do existing methods. Research limitations/implications – The focus of the paper is on the Heston and non-Heston leverage parameters. Practical implications – Finite sample simulation results show that the proposed estimator delivers more accurate estimates of the leverage parameter than do existing methods. Social implications – The research findings are important for the analysis of ultra high-frequency financial data. Originality/value – The paper provides a framework for using intraday high-frequency data of both indices' estimates, in particular, for improving the estimation accuracy of the leverage parameter, that is, the correlation between the two Brownian motions driving the diffusive components of the price process and its spot variance process, respectively.