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Multivariate Stochastic Volatility with Dynamic Cross Leverage

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  • Trojan, Sebastian

Abstract

WA multivariate stochastic volatility (MSV) model based on a Cholesky-type decomposition of the covariance matrix to model dynamic correlation in the observation and transition error as well as in cross leverage terms is proposed. The empirically relevant asymmetric concept of cross leverage is defined as a nonzero correlation between the ith asset return at time t and the jth log-volatility at time t+1. Volatilities and covariances are modeled separately, which makes an interpretation of leverage parameters straightforward. The model is applied on a three-dimensional portfolio consisting of the S&P 500 sector indices Financials, Industrials and Healthcare, spanning the recent financial crisis 2008/09. During and in the aftermath of market turmoil, increased cross leverage effects, higher unconditional kurtosis and stronger correlated information flow are observed. However, there is risk of overfitting and restricting time variation to elements governing dynamics of the observation error may be advisable.

Suggested Citation

  • Trojan, Sebastian, 2014. "Multivariate Stochastic Volatility with Dynamic Cross Leverage," Economics Working Paper Series 1424, University of St. Gallen, School of Economics and Political Science.
    • Handle: RePEc:usg:econwp:2014:24
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    File URL: http://ux-tauri.unisg.ch/RePEc/usg/econwp/EWP-1424.pdf
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    Cited by:

    1. Yuta Kurose & Yasuhiro Omori, "undated". "Multiple-lock Dynamic Equicorrelations with Realized Measures, Leverage and Endogeneity," CIRJE F-Series CIRJE-F-1075, CIRJE, Faculty of Economics, University of Tokyo.
    2. Shirota, Shinichiro & Omori, Yasuhiro & F. Lopes, Hedibert. & Piao, Haixiang, 2017. "Cholesky realized stochastic volatility model," Econometrics and Statistics, Elsevier, vol. 3(C), pages 34-59.
    3. Kurose, Yuta & Omori, Yasuhiro, 2020. "Multiple-block dynamic equicorrelations with realized measures, leverage and endogeneity," Econometrics and Statistics, Elsevier, vol. 13(C), pages 46-68.
    4. Yuta Kurose & Yasuhiro Omori, 2016. "Multiple-block Dynamic Equicorrelations with Realized Measures, Leverage and Endogeneity," CIRJE F-Series CIRJE-F-1024, CIRJE, Faculty of Economics, University of Tokyo.

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    More about this item

    Keywords

    Multivariate stochastic volatility; dynamic correlation; cross leverage; Cholesky decomposition; nonlinear state space model; Markov chain Monte Carlo; block sampler; particle filter;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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