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Stochastic Volatility: Univariate and Multivariate Extensions

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  • Eric Jacquier
  • Nicholas G. Polson
  • Peter E. Rossi

Abstract

Discrete time stochastic volatility models (hereafter SVOL) are noticeably more difficult to estimate than the successful ARCH family of models. In this paper we demonstrate efficient estimation and prediction for a number of univariate and multivariate SVOL models. Namely, we model fat-tailed and skewed conditional distributions, correlated errors distributions (leverage effect), and two multivariate models, a stochastic factor-structure model and a stochastic discount dynamic model. These extensions to the basic model are needed if one wants, for example, to compare SVOL models with ARCH-style models or to implement option pricing and portfolio selection under stochastic volatility. We specify the models as a hierarchy of conditional probability distributions: Pr(data | volatilities), Pr(volatilities | parameters) and Pr(parameters). This conceptually simple methodology provides a natural environment for the construction of stochastic volatility models that depart from standard distributional assumptions. Given a model and the data, inference and prediction are based on the joint posterior distribution of the volatilities and the parameters that we simulate via Markov chain Monte Carlo (MCMC) methods. Our approach also provides a sensitivity analysis for parameter inference and an outlier diagnostic. We estimate the model for several financial time series and find that the extensions considered are indeed needed. For the SVOL model we find strong evidence of non-normal conditional distributions for stock returns and exchange rates. We also find evidence of correlated errors for stock returns.
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Suggested Citation

  • Eric Jacquier & Nicholas G. Polson & Peter E. Rossi, 1999. "Stochastic Volatility: Univariate and Multivariate Extensions," CIRANO Working Papers 99s-26, CIRANO.
  • Handle: RePEc:cir:cirwor:99s-26
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    File URL: https://cirano.qc.ca/files/publications/99s-26.pdf
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Stochastic volatility; ARCH; MCMC algorithm; leverage effect; risk management; fat-tailed distributions; Volatilité stochastique; ARCH; algorithme MCMC; effets de levier; gestion de risque; distributions à queues épaisses;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • 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
    • G1 - Financial Economics - - General Financial Markets

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