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Value-at Risk under Measurement Error

Author

Listed:
  • Mohamed Doukali
  • Xiaojun Song
  • Abderrahim Taamouti

Abstract

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

Suggested Citation

  • Mohamed Doukali & Xiaojun Song & Abderrahim Taamouti, 2022. "Value-at Risk under Measurement Error," Working Papers 202209, University of Liverpool, Department of Economics.
    • Handle: RePEc:liv:livedp:202209
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Deconvolution kernel; Fourier transform; measurement errors; market microstructure noise; optimization; Value-at-Risk;
    All these keywords.

    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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