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VAR and ES/CVAR Dependence on data cleaning and Data Models: Analysis and Resolution

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  • Chris Kenyon
  • Andrew Green

Abstract

Historical (Stressed-) Value-at-Risk ((S)VAR), and Expected Shortfall (ES), are widely used risk measures in regulatory capital and Initial Margin, i.e. funding, computations. However, whilst the definitions of VAR and ES are unambiguous, they depend on input distributions that are data-cleaning- and Data-Model-dependent. We quantify the scale of these effects from USD CDS (2004--2014), and from USD interest rates (1989--2014, single-curve setup before 2004, multi-curve setup after 2004), and make two standardisation proposals: for data; and for Data-Models. VAR and ES are required for lifetime portfolio calculations, i.e. collateral calls, which cover a wide range of market states. Hence we need standard, i.e. clean, complete, and common (i.e. identical for all banks), market data also covering this wide range of market states. This data is historically incomplete and not clean hence data standardization is required. Stressed VAR and ES require moving market movements during a past (usually not recent) window to current, and future, market states. All choices (e.g. absolute difference, relative, relative scaled by some function of market states) implicitly define a Data Model for transformation of extreme market moves (recall that 99th percentiles are typical, and the behaviour of the rest is irrelevant). Hence we propose standard Data Models. These are necessary because different banks have different stress windows. Where there is no data, or a requirement for simplicity, we propose standard lookup tables (one per window, etc.). Without this standardization of data and Data Models we demonstrate that VAR and ES are complex derivatives of subjective choices.

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  • Chris Kenyon & Andrew Green, 2014. "VAR and ES/CVAR Dependence on data cleaning and Data Models: Analysis and Resolution," Papers 1405.7611, arXiv.org.
    • Handle: RePEc:arx:papers:1405.7611
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    References listed on IDEAS

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    1. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 593-606.
    2. Rosario Dell’Aquila & Paul Embrechts, 2006. "Extremes and Robustness: A Contradiction?," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 20(1), pages 103-118, April.
    3. Nick Deguillaume & Riccardo Rebonato & Andrey Pogudin, 2013. "The nature of the dependence of the magnitude of rate moves on the rates levels: a universal relationship," Quantitative Finance, Taylor & Francis Journals, vol. 13(3), pages 351-367, February.
    4. Andrew Green & Chris Kenyon, 2014. "KVA: Capital Valuation Adjustment," Papers 1405.0515, arXiv.org, revised Oct 2014.
    5. Imre Kondor, 2014. "Estimation Error of Expected Shortfall," Papers 1402.5534, arXiv.org.
    6. Kondor, Imre & Pafka, Szilard & Nagy, Gabor, 2007. "Noise sensitivity of portfolio selection under various risk measures," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1545-1573, May.
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    Cited by:

    1. Andrew Green & Chris Kenyon, 2014. "MVA: Initial Margin Valuation Adjustment by Replication and Regression," Papers 1405.0508, arXiv.org, revised Jan 2015.

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