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

Estimating the leverage parameter of continuous‐time stochastic volatility models using high... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Managerial Finance Emerald Publishing

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

Managerial Finance , Volume 37 (11): 20 – Sep 27, 2011

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Publisher
Emerald Publishing
Copyright
Copyright © 2011 Emerald Group Publishing Limited. All rights reserved.
ISSN
0307-4358
DOI
10.1108/03074351111167938
Publisher site
See Article on Publisher Site

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.

Journal

Managerial FinanceEmerald Publishing

Published: Sep 27, 2011

Keywords: Volatility; Stock prices; Gearing; Continuous time; High‐frequency data; Stochastic volatility; Implied volatility; S&P500; VIX

References