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Theoretical Sensitivity Analysis for Quantitative Operational Risk Management

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  • Takashi Kato

Abstract

We study the asymptotic behavior of the difference between the values at risk VaR(L) and VaR(L+S) for heavy tailed random variables L and S for application in sensitivity analysis of quantitative operational risk management within the framework of the advanced measurement approach of Basel II (and III). Here L describes the loss amount of the present risk profile and S describes the loss amount caused by an additional loss factor. We obtain different types of results according to the relative magnitudes of the thicknesses of the tails of L and S. In particular, if the tail of S is sufficiently thinner than the tail of L, then the difference between prior and posterior risk amounts VaR(L+S) - VaR(L) is asymptotically equivalent to the expectation (expected loss) of S.

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  • Takashi Kato, 2011. "Theoretical Sensitivity Analysis for Quantitative Operational Risk Management," Papers 1104.0359, arXiv.org, revised May 2017.
    • Handle: RePEc:arx:papers:1104.0359
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    1. Winfried G. Hallerbach, 1999. "Decomposing Portfolio Value-at-Risk: A General Analysis," Tinbergen Institute Discussion Papers 99-034/2, Tinbergen Institute.
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    Cited by:

    1. Takashi Kato, 2017. "Asymptotic Analysis for Spectral Risk Measures Parameterized by Confidence Level," Papers 1711.07335, arXiv.org.

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