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Bayesian Risk Forecasting for Long Horizons

Author

Listed:
  • Agnieszka Borowska

    (VU Amsterdam)

  • Lennart Hoogerheide

    (VU Amsterdam)

  • Siem Jan Koopman

    (VU Amsterdam)

Abstract
We present an accurate and efficient method for Bayesian forecasting of two financial risk measures, Value-at-Risk and Expected Shortfall, for a given volatility model. We obtain precise forecasts of the tail of the distribution of returns not only for the 10-days-ahead horizon required by the Basel Committee but even for long horizons, like one-month or one-year-ahead. The latter has recently attracted considerable attention due to the different properties of short term risk and long run risk. The key insight behind our importance sampling based approach is the sequential construction of marginal and conditional importance densities for consecutive periods. We report substantial accuracy gains for all the considered horizons in empirical studies on two datasets of daily financial returns, including a highly volatile period of the recent financial crisis. To illustrate the flexibility of the proposed construction method, we present how it can be adjusted to the frequentist case, for which we provide counterparts of both Bayesian applications.

Suggested Citation

  • Agnieszka Borowska & Lennart Hoogerheide & Siem Jan Koopman, 2019. "Bayesian Risk Forecasting for Long Horizons," Tinbergen Institute Discussion Papers 19-018/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20190018
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    File URL: https://papers.tinbergen.nl/19018.pdf
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    References listed on IDEAS

    as
    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Hoogerheide, Lennart & Opschoor, Anne & van Dijk, Herman K., 2012. "A class of adaptive importance sampling weighted EM algorithms for efficient and robust posterior and predictive simulation," Journal of Econometrics, Elsevier, vol. 171(2), pages 101-120.
    3. Pitt, Michael K. & Silva, Ralph dos Santos & Giordani, Paolo & Kohn, Robert, 2012. "On some properties of Markov chain Monte Carlo simulation methods based on the particle filter," Journal of Econometrics, Elsevier, vol. 171(2), pages 134-151.
    4. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    5. Hoogerheide, Lennart & van Dijk, Herman K., 2010. "Bayesian forecasting of Value at Risk and Expected Shortfall using adaptive importance sampling," International Journal of Forecasting, Elsevier, vol. 26(2), pages 231-247, April.
    6. Hoogerheide, Lennart F. & Kaashoek, Johan F. & van Dijk, Herman K., 2007. "On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: An application of flexible sampling methods using neural networks," Journal of Econometrics, Elsevier, vol. 139(1), pages 154-180, July.
    7. H. Kahn & A. W. Marshall, 1953. "Methods of Reducing Sample Size in Monte Carlo Computations," Operations Research, INFORMS, vol. 1(5), pages 263-278, November.
    8. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    9. Francis X. Diebold & Andrew Hickman & Atsushi Inoue & Til Schuermann, 1997. "Converting 1-Day Volatility to h-Day Volatitlity: Scaling by Root-h is Worse Than You Think," Center for Financial Institutions Working Papers 97-34, Wharton School Center for Financial Institutions, University of Pennsylvania.
    10. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Bayesian inference; forecasting; importance sampling; numerical accuracy; long run risk; Value-at-Risk; Expected Shortfall;
    All these keywords.

    JEL classification:

    • 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

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