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On Leverage in a Stochastic Volatility Model

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Author Info
Jun Yu () (School of Economics and Social Sciences, Singapore Management University)

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Abstract

This paper is concerned with specification for modelling financial leverage effect in the context of stochastic volatility (SV) models. Two alternative specifications coexist in the literature. One is the Euler approximation to the well known continuous time SV model with leverage effect and the other is the discrete time SV model of Jacquier, Polson and Rossi (2004, Journal of Econometrics, forthcoming). Using a Gaussian nonlinear state space form with uncorrelated measurement and transition errors, I show that it is easy to interpret the leverage effect in the conventional model whereas it is not clear how to obtain the leverage effect in the model of Jacquier et al. Empirical comparisons of these two models via Bayesian Markov chain Monte Carlo (MCMC) methods reveal that the specification of Jacquier et al is inferior. Simulation experiments are conducted to study the sampling properties of the Bayes MCMC for the conventional model. the appropriateness of statistical arbitrage as a test of marketefficiency.

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Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 13-2004.

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Length: 19 pages
Date of creation: Apr 2004
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Publication status: Published in SMU Economics and Statistics Working Paper Series
Handle: RePEc:siu:wpaper:13-2004

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Related research
Keywords: Bayes factors; Leverage effect; Markov chain Monte Carlo; Nonlinear state space models; Quasi maximum likelihood.;

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Find related papers by JEL classification:
C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

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  1. Federico M. Bandi & Roberto Reno, 2009. "Nonparametric Stochastic Volatility," Global COE Hi-Stat Discussion Paper Series gd08-035, Institute of Economic Research, Hitotsubashi University. [Downloadable!]
  2. Adam Clements & Stan Hurn & Scott White, 2006. "Estimating Stochastic Volatility Models Using a Discrete Non-linear Filter. Working paper #3," NCER Working Paper Series 3, National Centre for Econometric Research. [Downloadable!]
  3. Manabu Asai & Michael McAleer, 2005. "Asymmetric Multivariate Stochastic Volatility," DEA Working Papers 12, Universitat de les Illes Balears, Departament d'Economía Aplicada. [Downloadable!]
  4. Bent Jesper Christensen & Morten Ørregaard Nielsen, 2007. "The Effect of Long Memory in Volatility on Stock Market Fluctuations," CREATES Research Papers 2007-03, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
  5. Mark J Jensen & John M Maheu, 2008. "Bayesian semiparametric stochastic volatility modeling," Working Papers tecipa-314, University of Toronto, Department of Economics. [Downloadable!]
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  6. Yasuhiro Omori & Siddhartha Chib & Neil Shephard & Jouchi Nakajima, 2004. "Stochastic Volatility with Leverage: Fast Likelihood Inference," CIRJE F-Series CIRJE-F-297, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
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  7. Dinghai Xu, 2009. "The Applications of Mixtures of Normal Distributions in Empirical Finance: A Selected Survey," Working Papers 0904, University of Waterloo, Department of Economics, revised Sep 2009. [Downloadable!]
  8. Esther Ruiz & Helena Veiga, 2006. "Modelling Long-Memory Volatilities With Leverage Effect: Almsv Versus Fiegarch," Statistics and Econometrics Working Papers ws066016, Universidad Carlos III, Departamento de Estadística y Econometría. [Downloadable!]
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  9. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  10. Almut E. D. Veraart & Luitgard A. M. Veraart, 2009. "Stochastic volatility and stochastic leverage," CREATES Research Papers 2009-20, School of Economics and Management, University of Aarhus. [Downloadable!]
  11. Almut E. D. Veraart, 2008. "Impact of time–inhomogeneous jumps and leverage type effects on returns and realised variances," CREATES Research Papers 2008-57, School of Economics and Management, University of Aarhus. [Downloadable!]
  12. Dinghai Xu & John Knight & Tony S. Wirjanto, 2008. "Asymmetric Stochastic Conditional Duration Model --A Mixture of Normals Approach"," Working Papers 08007, University of Waterloo, Department of Economics. [Downloadable!]
  13. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2007. "Multivariate stochastic volatility," CIRJE F-Series CIRJE-F-488, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  14. Ole E. Barndorff-Nielsen & Almut E. D. Veraart, 2009. "Stochastic volatility of volatility in continuous time," CREATES Research Papers 2009-25, School of Economics and Management, University of Aarhus. [Downloadable!]
  15. Fulvia Focker & Umberto Triacca, 2006. "A new proxy of the average volatility of a basket of returns: A Monte Carlo study," Economics Bulletin, Economics Bulletin, vol. 3(15), pages 1-14. [Downloadable!]
  16. Bent Jesper Christensen & Morten Ørregaard Nielsen & Jie Zhu, 2007. "Long Memory in Stock Market Volatility and the Volatility-in-Mean Effect: The FIEGARCH-M Model," CREATES Research Papers 2007-10, School of Economics and Management, University of Aarhus. [Downloadable!]
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  17. Borus Jungbacker & Siem Jan Koopman, 2005. "On Importance Sampling for State Space Models," Tinbergen Institute Discussion Papers 05-117/4, Tinbergen Institute. [Downloadable!]
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