IDEAS home Printed from https://ideas.repec.org/a/spt/apfiba/v13y2023i1f13_1_6.html
   My bibliography  Save this article

Value-at-Risk Estimation Using an Interpolated Distribution of Financial Returns Series

Author

Listed:
  • Saeed Shaker-Akhtekhane
  • Solmaz Poorabbas

Abstract

This paper develops a model for estimating Value-at-Risk (VaR) from the historical return series. The proposed method uses spline interpolation to represent the empirical probability distribution of the return series. The approach developed in this paper is easy to implement using available programming platforms, and it can be generalized to other applications that involve estimating empirical distribution. In order to check the validity of the model, we use established back-testing methods and show that the model is robust to the changes in sample size and significance levels used to estimate VaR. We test the model against some similar distribution-based models using historical data from S&P500 index. We show that Value-at-Risk estimation based on the proposed method can outperform common historical, parametric, and kernel-based methods. As a result, the method can be useful in the context of validation of market risk models. Â JEL classification numbers: C52, C63, G17, G32.

Suggested Citation

  • Saeed Shaker-Akhtekhane & Solmaz Poorabbas, 2023. "Value-at-Risk Estimation Using an Interpolated Distribution of Financial Returns Series," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 13(1), pages 1-6.
    • Handle: RePEc:spt:apfiba:v:13:y:2023:i:1:f:13_1_6
    as

    Download full text from publisher

    File URL: http://www.scienpress.com/Upload/JAFB%2fVol%2013_1_6.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Huang, Alex YiHou, 2010. "An optimization process in Value-at-Risk estimation," Review of Financial Economics, Elsevier, vol. 19(3), pages 109-116, August.
    2. Danielsson, Jon, 2002. "The emperor has no clothes: Limits to risk modelling," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1273-1296, July.
    3. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    4. Hang Chan, Ngai & Deng, Shi-Jie & Peng, Liang & Xia, Zhendong, 2007. "Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations," Journal of Econometrics, Elsevier, vol. 137(2), pages 556-576, April.
    5. Saeed Shaker Akhtekhane & Parastoo Mohammadi, 2012. "Measuring Exchange Rate Fluctuations Risk Using the Value-at-Risk," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 2(3), pages 1-4.
    6. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    7. Alex YiHou Huang, 2010. "An optimization process in Value‐at‐Risk estimation," Review of Financial Economics, John Wiley & Sons, vol. 19(3), pages 109-116, August.
    8. Wei Sun & Svetlozar Rachev & Frank J. Fabozzi, 2009. "A New Approach for Using Lévy Processes for Determining High‐Frequency Value‐at‐Risk Predictions," European Financial Management, European Financial Management Association, vol. 15(2), pages 340-361, March.
    9. Carl Lonnbark, 2010. "A corrected Value-at-Risk predictor," Applied Economics Letters, Taylor & Francis Journals, vol. 17(12), pages 1193-1196.
    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. Stavros Degiannakis & Pamela Dent & Christos Floros, 2014. "A Monte Carlo Simulation Approach to Forecasting Multi-period Value-at-Risk and Expected Shortfall Using the FIGARCH-skT Specification," Manchester School, University of Manchester, vol. 82(1), pages 71-102, January.
    2. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    3. James M. O'Brien & Pawel J. Szerszen, 2014. "An Evaluation of Bank VaR Measures for Market Risk During and Before the Financial Crisis," Finance and Economics Discussion Series 2014-21, Board of Governors of the Federal Reserve System (U.S.).
    4. 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.
    5. Nieto, María Rosa & Ruiz Ortega, Esther, 2008. "Measuring financial risk : comparison of alternative procedures to estimate VaR and ES," DES - Working Papers. Statistics and Econometrics. WS ws087326, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    7. Gregory, Allan W. & Reeves, Jonathan J., 2008. "Interpreting Value at Risk (VaR) forecasts," Economic Systems, Elsevier, vol. 32(2), pages 167-176, June.
    8. Giovanni Barone‐Adesi & Chiara Legnazzi & Carlo Sala, 2019. "Option‐implied risk measures: An empirical examination on the S&P 500 index," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 24(4), pages 1409-1428, October.
    9. Boucher, Christophe M. & Daníelsson, Jón & Kouontchou, Patrick S. & Maillet, Bertrand B., 2014. "Risk models-at-risk," Journal of Banking & Finance, Elsevier, vol. 44(C), pages 72-92.
    10. Anjum, Hassan & Malik, Farooq, 2020. "Forecasting risk in the US Dollar exchange rate under volatility shifts," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    11. Lin, Edward M.H. & Sun, Edward W. & Yu, Min-Teh, 2020. "Behavioral data-driven analysis with Bayesian method for risk management of financial services," International Journal of Production Economics, Elsevier, vol. 228(C).
    12. 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.
    13. Edward W. Sun & Yu-Jen Wang & Min-Teh Yu, 2018. "Integrated Portfolio Risk Measure: Estimation and Asymptotics of Multivariate Geometric Quantiles," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 627-652, August.
    14. Takahashi, Makoto & Watanabe, Toshiaki & Omori, Yasuhiro, 2016. "Volatility and quantile forecasts by realized stochastic volatility models with generalized hyperbolic distribution," International Journal of Forecasting, Elsevier, vol. 32(2), pages 437-457.
    15. Polanski, Arnold & Stoja, Evarist, 2017. "Forecasting multidimensional tail risk at short and long horizons," International Journal of Forecasting, Elsevier, vol. 33(4), pages 958-969.
    16. Alin Marius Andrieş & Simona Nistor, 2018. "Systemic Risk and Foreign Currency Positions of Banks: Evidence from Emerging Europe," Eastern European Economics, Taylor & Francis Journals, vol. 56(5), pages 382-421, September.
    17. Alexander, Carol & Sheedy, Elizabeth, 2008. "Developing a stress testing framework based on market risk models," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2220-2236, October.
    18. Xun Lu & Kin Lai & Liang Liang, 2014. "Portfolio value-at-risk estimation in energy futures markets with time-varying copula-GARCH model," Annals of Operations Research, Springer, vol. 219(1), pages 333-357, August.
    19. Gonzalo Cortazar & Alejandro Bernales & Diether Beuermann, 2005. "Methodology and Implementation of Value-at-Risk Measures in Emerging Fixed-Income Markets with Infrequent Trading," Finance 0512030, University Library of Munich, Germany.
    20. Stavros Degiannakis & Apostolos Kiohos, 2014. "Multivariate modelling of 10-day-ahead VaR and dynamic correlation for worldwide real estate and stock indices," Journal of Economic Studies, Emerald Group Publishing Limited, vol. 41(2), pages 216-232, March.

    More about this item

    Keywords

    Value-at-Risk; Non-parametric estimation; Empirical distribution; Spline Interpolation.;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

    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:spt:apfiba:v:13:y:2023:i:1:f:13_1_6. 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: Eleftherios Spyromitros-Xioufis (email available below). General contact details of provider: http://www.scienpress.com/ .

    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.