IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb649/sfb649dp2006-078.html
   My bibliography  Save this paper

GHICA: Risk analysis with GH distributions and independent components

Author

Listed:
  • Chen, Ying
  • Härdle, Wolfgang Karl
  • Spokoiny, Vladimir

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.

Suggested Citation

  • Chen, Ying & Härdle, Wolfgang Karl & Spokoiny, Vladimir, 2006. "GHICA: Risk analysis with GH distributions and independent components," SFB 649 Discussion Papers 2006-078, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2006-078
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/25161/1/52256352X.PDF
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    2. Chen, Ying & Härdle, Wolfgang & Jeong, Seok-Oh, 2008. "Nonparametric Risk Management With Generalized Hyperbolic Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 910-923.
    3. Wolfgang Hardle & Helmut Herwartz & Vladimir Spokoiny, 2003. "Time Inhomogeneous Multiple Volatility Modeling," Journal of Financial Econometrics, Oxford University Press, vol. 1(1), pages 55-95.
    4. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook0501, December.
    5. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    6. Belomestny, Denis & Spokoiny, Vladimir, 2006. "Spatial aggregation of local likelihood estimates with applications to classification," SFB 649 Discussion Papers 2006-036, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH," NBER Working Papers 8554, National Bureau of Economic Research, Inc.
    8. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:hum:wpaper:sfb649dp2006-078 is not listed on IDEAS
    2. 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.
    3. Herwartz, Helmut & Golosnoy, Vasyl, 2007. "Semiparametric Approaches to the Prediction of Conditional Correlation Matrices in Finance," Economics Working Papers 2007-23, Christian-Albrechts-University of Kiel, Department of Economics.
    4. Giovanni Barone-Adesi & Francesco Audrino, 2006. "Average conditional correlation and tree structures for multivariate GARCH models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(8), pages 579-600.
    5. Christodoulakis, George A., 2007. "Common volatility and correlation clustering in asset returns," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1263-1284, November.
    6. Yusui Tang & Feng Ma & Yaojie Zhang & Yu Wei, 2022. "Forecasting the oil price realized volatility: A multivariate heterogeneous autoregressive model," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(4), pages 4770-4783, October.
    7. Baruník, Jozef & Kočenda, Evžen & Vácha, Lukáš, 2016. "Asymmetric connectedness on the U.S. stock market: Bad and good volatility spillovers," Journal of Financial Markets, Elsevier, vol. 27(C), pages 55-78.
    8. Rim Ammar Lamouchi & Ruba Khalid Shira, 2023. "Heterogeneous Behavior and Volatility Transmission in the Forex Market using High-Frequency Data," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 13(3), pages 1-3.
    9. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2006. "Analysis of high dimensional multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 134(2), pages 341-371, October.
    10. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
    11. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, September.
    12. Smile Dube, 2019. "GARCH Modelling of Conditional Correlations and Volatility of Exchange rates in BRICS Countries," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 9(1), pages 1-7.
    13. Pelletier, Denis, 2006. "Regime switching for dynamic correlations," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 445-473.
    14. Fengler, Matthias R. & Okhrin, Ostap, 2016. "Managing risk with a realized copula parameter," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 131-152.
    15. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    16. Cavit Pakel & Neil Shephard & Kevin Sheppard & Robert F. Engle, 2021. "Fitting Vast Dimensional Time-Varying Covariance Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(3), pages 652-668, July.
    17. Papaioannou, Elias & Portes, Richard & Siourounis, Gregorios, 2006. "Optimal currency shares in international reserves: The impact of the euro and the prospects for the dollar," Journal of the Japanese and International Economies, Elsevier, vol. 20(4), pages 508-547, December.
    18. Green, Rikard & Larsson, Karl & Lunina, Veronika & Nilsson, Birger, 2018. "Cross-commodity news transmission and volatility spillovers in the German energy markets," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 231-243.
    19. Yu‐Sheng Lai, 2022. "High‐frequency data and stock–bond investing," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(8), pages 1623-1638, December.
    20. Ben Tims & Ronald Mahieu, 2006. "A Range-Based Multivariate Stochastic Volatility Model for Exchange Rates," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 409-424.
    21. Nicola, Francesca de & De Pace, Pierangelo & Hernandez, Manuel A., 2016. "Co-movement of major energy, agricultural, and food commodity price returns: A time-series assessment," Energy Economics, Elsevier, vol. 57(C), pages 28-41.

    More about this item

    Keywords

    multivariate risk management; independent component analysis; generalized hyperbolic distribution; local exponential estimation; value at risk; expected shortfall;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: 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
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G20 - Financial Economics - - Financial Institutions and Services - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:sfb649:sfb649dp2006-078. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sohubde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.