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Avoiding zero probability events when computing Value at Risk contributions

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  • Takaaki Koike
  • Yuri F. Saporito
  • Rodrigo S. Targino

Abstract

This paper is concerned with the process of risk allocation for a generic multivariate model when the risk measure is chosen as the Value-at-Risk (VaR). We recast the traditional Euler contributions from an expectation conditional on an event of zero probability to a ratio involving conditional expectations whose conditioning events have strictly positive probability. We derive an analytical form of the proposed representation of VaR contributions for various parametric models. Our numerical experiments show that the estimator using this novel representation outperforms the standard Monte Carlo estimator in terms of bias and variance. Moreover, unlike the existing estimators, the proposed estimator is free from hyperparameters under a parametric setting.

Suggested Citation

  • Takaaki Koike & Yuri F. Saporito & Rodrigo S. Targino, 2020. "Avoiding zero probability events when computing Value at Risk contributions," Papers 2004.13235, arXiv.org, revised Jun 2022.
    • Handle: RePEc:arx:papers:2004.13235
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    Cited by:

    1. Silvana M. Pesenti & Pietro Millossovich & Andreas Tsanakas, 2023. "Differential Sensitivity in Discontinuous Models," Papers 2310.06151, arXiv.org.
    2. Takaaki Koike & Cathy W. S. Chen & Edward M. H. Lin, 2024. "Forecasting and Backtesting Gradient Allocations of Expected Shortfall," Papers 2401.11701, arXiv.org.
    3. Akif Ince & Ilaria Peri & Silvana Pesenti, 2021. "Risk contributions of lambda quantiles," Papers 2106.14824, arXiv.org, revised Nov 2022.

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    More about this item

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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