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CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation

Author

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  • Simon A. BRODA

    (University of Zurich, Swiss Banking Institute)

  • Marc S. PAOLELLA

    (University of Zurich, Swiss Banking Institute)

Abstract

The estimation of multivariate GARCH models remains a challenging task, even in modern computer environments. This manuscript shows how Independent Component Analysis can be used to estimate the Generalized Orthogonal GARCH model in a fraction of the time otherwise required. The proposed method is a two-step procedure, separating the estimation of the correlation structure from that of the univariate dynamics, thus facilitating the incorporation of non-Gaussian innovations distributions in a straightforward manner. The generalized hyperbolic distribution provides an excellent parametric description of financial returns data and is used for the univariate fits, but its convolutions, necessary for portfolio risk calculations, are intractable. This restriction is overcome by a saddlepoint approximation to the required distribution function, which is computationally cheap and extremely accurate most notably in the tail, which is crucial for risk calculations. A simulation study and an application to stock returns demonstrate the validity of the procedure.

Suggested Citation

  • Simon A. BRODA & Marc S. PAOLELLA, 2008. "CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation," Swiss Finance Institute Research Paper Series 08-08, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp0808
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    Keywords

    Empirical Finance; Saddlepoint Approximation; Value at Risk;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • 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
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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