Template-type: ReDIF-Paper 1.0
Author-Name: Isao Ishida
Author-Person: pis93
Author-Workplace-Name: Center for the Study of Finance and Insurance Osaka University, Japan
Author-Name: Michael McAleer
Author-Person: pmc90
Author-Workplace-Name: Econometrisch Instituut (Econometric Institute), Faculteit der Economische 
	Wetenschappen (Erasmus School of Economics), Erasmus Universiteit, Tinbergen Instituut (Tinbergen Institute).
Author-Name: Kosuke Oya
Author-Workplace-Name: Graduate School of Economics and Center for the Study of Finance and Insurance
	Osaka University, Japan
Title: Estimating the Leverage Parameter of Continuous-time Stochastic Volatility Models Using High Frequency S&P 500 and VIX
Abstract: This paper proposes 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 of Exchange 
	(CBOE) implied (or expected) volatility index (VIX). Intraday high-frequency observations data have become readily 
	available for an increasing number of financial assets and their derivatives in recent years, but it is well known that 
	attempts to directly apply popular continuous-time models to short intraday time intervals, and estimate the parameters 
	using such data, can lead to nonsensical estimates due to severe intraday seasonality. A primary purpose of the paper is 
	to provide a framework for using intraday high frequency data of both the index estimate, in particular, for improving 
	the estimation accuracy of the leverage parameter, p, that is, the correlation between the two Brownian motions driving 
	the diffusive components of the price process and its spot variance process, respectively. As a special	case, we focus on 
	Heston’s (1993) square-root SV model, and propose the realized leverage estimator for p, noting that, under this model 
	without measurement errors, the “realized leverage,” or the realized covariation of the price and VIX processes divided 
	by the product of the realized volatilities of the two processes, is in-fill consistent for p. Finite sample simulation 
	results show that the proposed estimator delivers more accurate estimates of the leverage parameter than do existing 
	methods.
Classification-JEL: G13, G17, G32.
Keywords: Continuous time, high frequency data, stochastic volatility, S&P 500, implied volatility, VIX.
Note: The authors are most grateful to two referees for helpful comments and suggestions. The first author wishes 
	to thank Yusho Kaguraoka, Toshiaki Watanabe, and participants at the 2010 Annual Meeting of the Nippon 
	Finance Association, the CSFI Nakanoshima Workshop 2009, and the Hiroshima University of Economics 
	Financial Econometrics Workshop 2010 for valuable comments, and the Japan Society for the Promotion of 
	Science (Grants-in-Aid for Scientific Research No. 20530265) for financial support. The second author 
	is most grateful for the financial support of the Australian Research Council, National Science Council, 
	Taiwan, and the Japan Society for the Promotion of Science. The third author is thankful for Grants-in-Aid 
	for Scientific Research No. 22243021 from the Japan Society for the Promotion of Science.
Length: 34 pages 
Creation-Date: 2011 
Number: 2011-17
X-File-Ref: http://america.sim.ucm.es/repec/ucm/ref/doicae1117.txt
File-URL: https://eprints.ucm.es/id/eprint/12807/1/1117.pdf
File-Format: Application/pdf
File-Function: revised May 2011
Handle: RePEc:ucm:doicae:1117