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GHICA -- Risk analysis with GH distributions and independent components

Author

Listed:
  • Chen, Ying
  • Härdle, Wolfgang
  • Spokoiny, Vladimir
Abstract
Over recent years, a study on risk management has been prompted by the Basel committee for regular banking supervisory. There are however limitations of some widely-used risk management methods that either calculate risk measures under the Gaussian distributional assumption or involve numerical difficulty. The primary aim of this paper is to present a realistic and fast method, GHICA, which overcomes the limitations in multivariate risk analysis. The idea is to first retrieve independent components (ICs) out of the observed high-dimensional time series and then individually and adaptively fit the resulting ICs in the generalized hyperbolic (GH) distributional framework. For the volatility estimation of each IC, the local exponential smoothing technique is used to achieve the best possible accuracy of estimation. Finally, the fast Fourier transformation technique is used to approximate the density of the portfolio returns. The proposed GHICA method is applicable to covariance estimation as well. It is compared with the dynamic conditional correlation (DCC) method based on the simulated data with d = 50 GH distributed components. We further implement the GHICA method to calculate risk measures given 20-dimensional German DAX portfolios and a dynamic exchange rate portfolio. Several alternative methods are considered as well to compare the accuracy of calculation with the GHICA one.

Suggested Citation

  • Chen, Ying & Härdle, Wolfgang & Spokoiny, Vladimir, 2010. "GHICA -- Risk analysis with GH distributions and independent components," Journal of Empirical Finance, Elsevier, vol. 17(2), pages 255-269, March.
    • Handle: RePEc:eee:empfin:v:17:y:2010:i:2:p:255-269
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    References listed on IDEAS

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    Cited by:

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    2. Kumiega, Andrew & Neururer, Thaddeus & Van Vliet, Ben, 2011. "Independent component analysis for realized volatility: Analysis of the stock market crash of 2008," The Quarterly Review of Economics and Finance, Elsevier, vol. 51(3), pages 292-302, June.
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    5. 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.
    6. J. Hambuckers & C. Heuchenne, 2017. "A robust statistical approach to select adequate error distributions for financial returns," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(1), pages 137-161, January.
    7. 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.
    8. Schwaab, Bernd & Lucas, André & Zhang, Xin, 2013. "Conditional and joint credit risk," Working Paper Series 1621, European Central Bank.
    9. Tran Hoang Hai, 2020. "Estimation of volatility causality in structural autoregressions with heteroskedasticity using independent component analysis," Statistical Papers, Springer, vol. 61(1), pages 1-16, February.
    10. Wesselhöfft, Niels & Härdle, Wolfgang Karl, 2019. "Estimating low sampling frequency risk measure by high-frequency data," IRTG 1792 Discussion Papers 2019-003, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".

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