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CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation

Author

Listed:
  • 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, 2006. "CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation," Swiss Finance Institute Research Paper Series 08-08, Swiss Finance Institute, revised Feb 2008.
  • Handle: RePEc:chf:rpseri:rp0808
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    Cited by:

    1. Slim, Skander & Koubaa, Yosra & BenSaïda, Ahmed, 2017. "Value-at-Risk under Lévy GARCH models: Evidence from global stock markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 46(C), pages 30-53.
    2. Marc S. Paolella, 2016. "Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability," Econometrics, MDPI, Open Access Journal, vol. 4(2), pages 1-28, May.
    3. Michele Leonardo Bianchi & Gian Luca Tassinari & Frank J. Fabozzi, 2016. "Riding With The Four Horsemen And The Multivariate Normal Tempered Stable Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-28, June.
    4. Fajardo, José & Farias, Aquiles, 2010. "Derivative pricing using multivariate affine generalized hyperbolic distributions," Journal of Banking & Finance, Elsevier, vol. 34(7), pages 1607-1617, July.
    5. Broda, Simon A. & Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Stable mixture GARCH models," Journal of Econometrics, Elsevier, vol. 172(2), pages 292-306.
    6. Alp, Tansel & Demetrescu, Matei, 2010. "Joint forecasts of Dow Jones stocks under general multivariate loss function," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2360-2371, November.
    7. Alexios Ghalanos & Eduardo Rossi & Giovanni Urga, 2015. "Independent Factor Autoregressive Conditional Density Model," Econometric Reviews, Taylor & Francis Journals, vol. 34(5), pages 594-616, May.
    8. Zolotko, Mikhail & Okhrin, Ostap, 2014. "Modelling the general dependence between commodity forward curves," Energy Economics, Elsevier, vol. 43(C), pages 284-296.
    9. Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Time-varying mixture GARCH models and asymmetric volatility," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 602-623.
    10. Basher, Syed Abul & Sadorsky, Perry, 2016. "Hedging emerging market stock prices with oil, gold, VIX, and bonds: A comparison between DCC, ADCC and GO-GARCH," Energy Economics, Elsevier, vol. 54(C), pages 235-247.
    11. Matilainen, Markus & Nordhausen, Klaus & Oja, Hannu, 2015. "New independent component analysis tools for time series," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 80-87.
    12. repec:eee:ecmode:v:72:y:2018:i:c:p:278-295 is not listed on IDEAS
    13. repec:gam:jecnmx:v:5:y:2017:i:2:p:18-:d:97715 is not listed on IDEAS
    14. Paolella, Marc S., 2017. "Asymmetric stable Paretian distribution testing," Econometrics and Statistics, Elsevier, vol. 1(C), pages 19-39.

    More about this item

    Keywords

    Empirical Finance; Saddlepoint Approximation; Value at Risk;

    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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