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Comparing the Value at Risk Performance of the CreditRisk + and its Enhancement: A Large Deviations Approach

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  • Amogh Deshpande

    (Macquarie University)

Abstract

The standard CreditRisk + (CR + ) is a well-known default-mode credit risk model. An extension to the CR + that introduces correlation through a two-stage hierarchy of randomness has been discussed by Deshpande and Iyer (Central Eur J Oper Res 17(2):219–228, 2009) and more recently by Sowers (2010). It is termed the 2-stage CreditRisk + (2-CR + ) in the former. Unlike the standard CR + , the 2-CR + model is formulated to allow correlation between sectoral default rates through dependence on a common set of macroeconomic variables. Furthermore the default rates for a 2-CR + are distributed according to a general univariate distribution which is in stark contrast to the uniformly Gamma distributed sectoral default rates in the CR + . We would then like to understand the behaviour of these two models with regards to their computed Value at Risk (VaR) as the number of sectors and macroeconomic variables approaches infinity. In particular we would like to ask whether the 2-CR + produces higher VaR than the CR + and if so then for which type of credit portfolio. Utilizing the theory of Large deviations, we provide a methodology for comparing the Value at risk performance of these two competing models by computing certain associated rare event probabilities. In particular we show that the 2-Stage CR + definitely produces higher VaR than the CR + for a particular class of a credit portfolio which we term as a “balanced” credit portfolio. We support this statistical risk analysis through numerical examples.

Suggested Citation

  • Amogh Deshpande, 2014. "Comparing the Value at Risk Performance of the CreditRisk + and its Enhancement: A Large Deviations Approach," Methodology and Computing in Applied Probability, Springer, vol. 16(4), pages 1009-1023, December.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:4:d:10.1007_s11009-013-9345-8
    DOI: 10.1007/s11009-013-9345-8
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    References listed on IDEAS

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    1. Amogh Deshpande & Srikanth Iyer, 2009. "The credit risk + model with general sector correlations," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 17(2), pages 219-228, June.
    2. Giesecke, Kay & Weber, Stefan, 2006. "Credit contagion and aggregate losses," Journal of Economic Dynamics and Control, Elsevier, vol. 30(5), pages 741-767, May.
    3. Amir Dembo & Jean-Dominique Deuschel & Darrell Duffie, 2004. "Large portfolio losses," Finance and Stochastics, Springer, vol. 8(1), pages 3-16, January.
    4. Konstantinos Spiliopoulos & Richard B. Sowers, 2010. "Recovery Rates in investment-grade pools of credit assets: A large deviations analysis," Papers 1006.2711, arXiv.org, revised Aug 2011.
    5. Spiliopoulos, Konstantinos & Sowers, Richard B., 2011. "Recovery rates in investment-grade pools of credit assets: A large deviations analysis," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2861-2898.
    6. Paolo Dai Pra & Wolfgang J. Runggaldier & Elena Sartori & Marco Tolotti, 2007. "Large portfolio losses: A dynamic contagion model," Papers 0704.1348, arXiv.org, revised Mar 2009.
    7. Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
    8. Dai Pra, Paolo & Tolotti, Marco, 2009. "Heterogeneous credit portfolios and the dynamics of the aggregate losses," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2913-2944, September.
    9. Paul Glasserman & Wanmo Kang & Perwez Shahabuddin, 2007. "Large Deviations In Multifactor Portfolio Credit Risk," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 345-379, July.
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    Cited by:

    1. Papalamprou, Konstantinos & Antoniou, Paschalis, 2019. "Estimation of capital requirements in downturn conditions via the CBV model: Evidence from the Greek banking sector," Operations Research Perspectives, Elsevier, vol. 6(C).

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