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Value‐at‐Risk under Measurement Error

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  • Mohamed Doukali
  • Xiaojun Song
  • Abderrahim Taamouti

Abstract

We propose a method for estimating Value‐at‐Risk that corrects for the effect of measurement errors in stock prices. We show that the presence of measurement errors might pose serious problems for estimating risk measures. In particular, when stock prices are contaminated, existing estimators of Value‐at‐Risk are inconsistent and might lead to an underestimation of risk, which can result in extreme leverage ratios within the held portfolios. Using a Fourier transform and a deconvolution kernel estimator of the probability distribution function of actual latent prices, we derive a robust estimator of Value‐at‐Risk in the presence of measurement errors. Monte Carlo simulations and real data analysis illustrate satisfactory performance of the proposed method.

Suggested Citation

  • Mohamed Doukali & Xiaojun Song & Abderrahim Taamouti, 2024. "Value‐at‐Risk under Measurement Error," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(3), pages 690-713, June.
    • Handle: RePEc:bla:obuest:v:86:y:2024:i:3:p:690-713
    DOI: 10.1111/obes.12589
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    References listed on IDEAS

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    More about this item

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G19 - Financial Economics - - General Financial Markets - - - Other
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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