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CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation

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  • Simon A. Broda
  • Marc S. Paolella

Abstract

This paper 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 saddlepoint approximations for the Value at Risk and expected shortfall, which are computationally cheap and retain excellent accuracy far into the tails. It is further shown that the mean-expected shortfall portfolio optimization problem can be solved efficiently in the context of the model. A simulation study and an application to stock returns demonstrate the validity of the procedure. Copyright The Author 2009. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org., Oxford University Press.

Suggested Citation

  • Simon A. Broda & Marc S. Paolella, 2009. "CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation," Journal of Financial Econometrics, Oxford University Press, vol. 7(4), pages 412-436, Fall.
    • Handle: RePEc:oup:jfinec:v:7:y:2009:i:4:p:412-436
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbp011
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    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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