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

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.

Citation

Ishida, I., McAleer, M. and Oya, K. (2011), "Estimating the leverage parameter of continuous‐time stochastic volatility models using high frequency S&P 500 and VIX", Managerial Finance, Vol. 37 No. 11, pp. 1048-1067. https://doi.org/10.1108/03074351111167938