IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2605.10066.html

On the modeling assumptions of Historical Simulation for Value-at-Risk

Author

Listed:
  • Bjorn Lofdahl Grelsson

Abstract

Historical Simulation (HS) and its extensions form a popular class of methods for estimating Value-at-Risk for portfolios of financial assets based on historical data. In this note, we seek to unify several ideas and models from throughout the literature into a single modeling framework. By explicitly defining a parametric model form for the asset returns and extracting the realized increments of the driving innovation process from historical data, we are able to reproduce the Historical Simulation, filtered Historical Simulation, and displaced Historical Simulation methods. This shows beyond a doubt that these methods need more underlying assumptions than what is often alluded to.

Suggested Citation

  • Bjorn Lofdahl Grelsson, 2026. "On the modeling assumptions of Historical Simulation for Value-at-Risk," Papers 2605.10066, arXiv.org.
    • Handle: RePEc:arx:papers:2605.10066
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2605.10066
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Attilio Meucci, 2005. "Risk and Asset Allocation," Springer Finance, Springer, number 978-3-540-27904-4, March.
    2. Fries, Christian P. & Nigbur, Tobias & Seeger, Norman, 2017. "Displaced relative changes in historical simulation: Application to risk measures of interest rates with phases of negative rates," Journal of Empirical Finance, Elsevier, vol. 42(C), pages 175-198.
    3. Pritsker, Matthew, 2006. "The hidden dangers of historical simulation," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 561-582, February.
    4. Giovanni Barone‐Adesi & Kostas Giannopoulos & Les Vosper, 1999. "VaR without correlations for portfolios of derivative securities," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(5), pages 583-602, August.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Mark Lichtner, 2019. "How to choose the return model for market risk? Getting towards a right magnitude of stressed VaR," Quantitative Finance, Taylor & Francis Journals, vol. 19(8), pages 1391-1407, August.
    Full references (including those not matched with items on IDEAS)

    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. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    2. Fries, Christian P. & Nigbur, Tobias & Seeger, Norman, 2017. "Displaced relative changes in historical simulation: Application to risk measures of interest rates with phases of negative rates," Journal of Empirical Finance, Elsevier, vol. 42(C), pages 175-198.
    3. Jae‐Yun Jun & Victor Lebreton & Yves Rakotondratsimba, 2021. "Forecasting negative yield‐curve distributions," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(3), pages 367-386, April.
    4. Marco Gregnanin & Johannes De Smedt & Giorgio Gnecco & Maurizio Parton, 2026. "A Generative Adversarial Graph Neural Network for Synthetic Time Series Data," Papers 2605.22215, arXiv.org.
    5. Vladimir Rankovic & Mikica Drenovak & Branko Uroševic & Ranko Jelic, 2016. "Mean Univariate-GARCH VaR Portfolio Optimization: Actual Portfolio Approach," CESifo Working Paper Series 5731, CESifo.
    6. Kim Christensen & Mathias Siggaard & Bezirgen Veliyev, 2023. "A Machine Learning Approach to Volatility Forecasting," Journal of Financial Econometrics, Oxford University Press, vol. 21(5), pages 1680-1727.
    7. Laura Garcia‐Jorcano & Alfonso Novales, 2021. "Volatility specifications versus probability distributions in VaR forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 189-212, March.
    8. Chrétien, Stéphane & Coggins, Frank, 2010. "Performance and conservatism of monthly FHS VaR: An international investigation," International Review of Financial Analysis, Elsevier, vol. 19(5), pages 323-333, December.
    9. Meriem Rjiba & Michail Tsagris & Hedi Mhalla, 2015. "Bootstrap for Value at Risk Prediction," International Journal of Empirical Finance, Research Academy of Social Sciences, vol. 4(6), pages 362-371.
    10. Wu, Qi & Yan, Xing, 2019. "Capturing deep tail risk via sequential learning of quantile dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 109(C).
    11. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    12. Alejandro Bernales & Diether W. Beuermann & Gonzalo Cortazar, 2014. "Thinly traded securities and risk management," Estudios de Economia, University of Chile, Department of Economics, vol. 41(1 Year 20), pages 5-48, June.
    13. O’Brien, James & Szerszeń, Paweł J., 2017. "An evaluation of bank measures for market risk before, during and after the financial crisis," Journal of Banking & Finance, Elsevier, vol. 80(C), pages 215-234.
    14. Cheng, Wan-Hsiu & Hung, Jui-Cheng, 2011. "Skewness and leptokurtosis in GARCH-typed VaR estimation of petroleum and metal asset returns," Journal of Empirical Finance, Elsevier, vol. 18(1), pages 160-173, January.
    15. Alessandra Amendola & Vincenzo Candila & Antonio Naimoli & Giuseppe Storti, 2024. "Combining Value-at-Risk and Expected Shortfall forecasts via the Model Confidence Set," Papers 2406.06235, arXiv.org, revised Feb 2026.
    16. Shige Peng & Shuzhen Yang & Jianfeng Yao, 2018. "Improving Value-at-Risk prediction under model uncertainty," Papers 1805.03890, arXiv.org, revised Jun 2020.
    17. Benjamin R. Auer & Benjamin Mögel, 2016. "How Accurate are Modern Value-at-Risk Estimators Derived from Extreme Value Theory?," CESifo Working Paper Series 6288, CESifo.
    18. João Pedro M. Franco & Márcio Laurini, 2025. "Multivariate Risk Analysis in Cryptocurrency Market: An Optimal Transport Approach," Computational Economics, Springer;Society for Computational Economics, vol. 66(6), pages 5257-5298, December.
    19. El Bouhadi, Abdelhamid & Achibane, Khalid, 2009. "The Predictive Power of Conditional Models: What Lessons to Draw with Financial Crisis in the Case of Pre-Emerging Capital Markets?," MPRA Paper 19482, University Library of Munich, Germany.
    20. Su, Jung-Bin, 2014. "Empirical analysis of long memory, leverage, and distribution effects for stock market risk estimates," The North American Journal of Economics and Finance, Elsevier, vol. 30(C), pages 1-39.

    More about this item

    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:arx:papers:2605.10066. 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: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    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.