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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. 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.).
    4. 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.
    5. 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.
    6. Carl Lonnbark, 2010. "A corrected Value-at-Risk predictor," Applied Economics Letters, Taylor & Francis Journals, vol. 17(12), pages 1193-1196.
    7. 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.
    8. Danielsson, Jon, 2002. "The emperor has no clothes: Limits to risk modelling," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1273-1296, July.
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    Keywords

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    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

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