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GHICA - Risk Analysis with GH Distributions and Independent Components

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Author Info
Ying Chen
Wolfgang Härdle
Vladimir Spokoiny

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Abstract

Over recent years, 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.

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Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-078.

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Length: 32 pages
Date of creation: Nov 2006
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Handle: RePEc:hum:wpaper:sfb649dp2006-078

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Related research
Keywords: Multivariate Risk Management; Independent Component Analysis; Generalized Hyperbolic Distribution; Local Exponential Estimation; Value at Risk; Expected Shortfall.;

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: 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
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
G20 - Financial Economics - - Financial Institutions and Services - - - General

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References listed on IDEAS
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  2. Neville Francis & Valerie A. Ramey, 2006. "The Source of Historical Economic Fluctuations: An Analysis using Long-Run Restrictions," NBER Chapters, in: NBER International Seminar on Macroeconomics 2004, pages 17-74 National Bureau of Economic Research, Inc.
    Other versions:
  3. Christian Stoltenberg, 2006. "Real Balance Effects, Timing and Equilibrium Determination," SFB 649 Discussion Papers SFB649DP2006-073, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  4. Enzo Weber, 2006. "Common and Uncommon Sources of Growth in Asia Pacific," SFB 649 Discussion Papers SFB649DP2006-064, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  5. Enzo Weber, 2006. "The Euro and the Transatlantic Capital Market Leadership: A Recursive Cointegration Analysis," SFB 649 Discussion Papers SFB649DP2006-056, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  6. Benjamin Bental & Dominique Demougin, 2006. "Institutions, Bargaining Power and Labor Shares," SFB 649 Discussion Papers SFB649DP2006-009, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  8. Denis Belomestny & Vladimir Spokoiny, 2006. "Spatial aggregation of local likelihood estimates with applications to classification," SFB 649 Discussion Papers SFB649DP2006-036, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  11. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy Models [2]," SFB 649 Discussion Papers SFB649DP2006-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  12. Enzo Weber, 2006. "British Interest Rate Convergence Between The Us And Europe: A Recursive Cointegration Analysis," Icfai University Journal of Monetary Economics, Icfai Press, vol. 0(4), pages 29-47, November.
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  13. Dominique Demougin & Anja Schöttner, 2006. "Technological Choice under Organizational Diseconomies of Scale," SFB 649 Discussion Papers SFB649DP2006-028, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  14. Kurt Geppert & Martin Gornig & Axel Werwatz, 2006. "Economic Growth of Agglomerations and Geographic Concentration of Industries – Evidence for Germany," SFB 649 Discussion Papers SFB649DP2006-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  15. Ralf Brüggemann & Helmut Lütkepohl & Massimiliano Marcellino, 2006. "Forecasting Euro-Area Variables with German Pre-EMU Data," SFB 649 Discussion Papers SFB649DP2006-065, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  16. Harald Uhlig, 2006. "Approximate Solutions to Dynamic Models - Linear Methods," SFB 649 Discussion Papers SFB649DP2006-030, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  18. Szymon Borak & Wolfgang Härdle & Stefan Trück & Rafal Weron, 2006. "Convenience Yields for CO2 Emission Allowance Futures Contracts," SFB 649 Discussion Papers SFB649DP2006-076, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  19. Denis Belomestny & Grigori N. Milstein & Vladimir Spokoiny, 2006. "Regression methods in pricing American and Bermudan options using consumption processes," SFB 649 Discussion Papers SFB649DP2006-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  20. Enzo Giacomini & Michael Handel & Wolfgang K. Härdle, 2006. "Time Dependent Relative Risk Aversion," SFB 649 Discussion Papers SFB649DP2006-020, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  21. Bernd Görzig & Martin Gornig & Axel Werwatz, 2004. "East Germany's Wage Gap: A Non-Parametric Decomposition Based on Establishment Characteristics," Discussion Papers of DIW Berlin 451, DIW Berlin, German Institute for Economic Research. [Downloadable!]
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  22. Harald Uhlig, 2004. "Discussion of "The Source of Historical Economic Fluctuations: An Analysis using Long-Run Restrictions" by Neville Francis and Valerie A. Ramey," SFB 649 Discussion Papers SFB649DP2006-042, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised May 2006. [Downloadable!]
  23. Daniel Hernandez–Hernandez & Alexander Schied, 2006. "A Control Approach to Robust Utility Maximization with Logarithmic Utility and Time-Consistent Penalties," SFB 649 Discussion Papers SFB649DP2006-061, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  24. Dominique Demougin & Oliver Fabel, 2006. "The Division of Ownership in New Ventures," SFB 649 Discussion Papers SFB649DP2006-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  25. Ralf Brüggemann & Wolfgang Härdle & Julius Mungo & Carsten Trenkler, 2006. "VAR Modeling for Dynamic Semiparametric Factors of Volatility Strings," SFB 649 Discussion Papers SFB649DP2006-011, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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