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Multivariate stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck processes: A quasi-likelihood approach

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Abstract

This paper extends the ordinary quasi-likelihood estimator for stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck (OU) processes to vector processes. Despite the fact that multivariate modeling of asset returns is essential for portfolio optimization and risk management -- major areas of financial analysis -- the literature on multivariate modeling of asset prices in continuous time is sparse, both with regard to theoretical and applied results. This paper uses non-Gaussian OU-processes as building blocks for multivariate models for high frequency financial data. The OU framework allows exact discrete time transition equations that can be represented on a linear state space form. We show that a computationally feasible quasi-likelihood function can be constructed by means of the Kalman filter also in the case of high-dimensional vector processes. The framework is applied to Euro/NOK and US Dollar/NOK exchange rate data for the period 2.1.1989-4.2.2010.

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  • Arvid Raknerud & Øivind Skare, 2010. "Multivariate stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck processes: A quasi-likelihood approach," Discussion Papers 614, Statistics Norway, Research Department.
  • Handle: RePEc:ssb:dispap:614
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    File URL: https://www.ssb.no/a/publikasjoner/pdf/DP/dp614.pdf
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    Keywords

    multivariate stochastic volatility; exchange rates; Ornstein-Uhlenbeck processes; quasi-likelihood; factor models; state space representation;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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