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Model-free computation of risk contributions in credit portfolios

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  • Leitao, Álvaro
  • Ortiz-Gracia, Luis

Abstract

In this work, we propose a non-parametric density estimation technique for measuring the risk in a credit portfolio, aiming at efficiently computing the marginal risk contributions. The novel method is based on wavelets, and we derive closed-form expressions to calculate the Value-at-Risk (VaR), the Expected Shortfall (ES) as well as the individual risk contributions to VaR (VaRC) and ES (ESC). We consider the multi-factor Gaussian and t-copula models for driving the defaults. The results obtained along the numerical experiments show the impressive accuracy and speed of this method when compared with crude Monte Carlo simulation. The presented methodology applies in the same manner regardless of the used model, and the computational performance is invariant under a considerable change in the dimension of the selected model. The speed-up with respect to the classical Monte Carlo approach ranges from twenty-five to one-thousand depending on the used model.

Suggested Citation

  • Leitao, Álvaro & Ortiz-Gracia, Luis, 2020. "Model-free computation of risk contributions in credit portfolios," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    • Handle: RePEc:eee:apmaco:v:382:y:2020:i:c:s0096300320303155
    DOI: 10.1016/j.amc.2020.125351
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    References listed on IDEAS

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    1. Dirk Tasche, 2009. "Capital allocation for credit portfolios with kernel estimators," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 581-595.
    2. Michael Kalkbrener, 2005. "An Axiomatic Approach To Capital Allocation," Mathematical Finance, Wiley Blackwell, vol. 15(3), pages 425-437, July.
    3. Marek Rutkowski & Silvio Tarca, 2015. "Regulatory Capital Modeling For Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-44.
    4. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    5. Paul Glasserman & Jingyi Li, 2005. "Importance Sampling for Portfolio Credit Risk," Management Science, INFORMS, vol. 51(11), pages 1643-1656, November.
    6. Guangwu Liu, 2015. "Simulating Risk Contributions of Credit Portfolios," Operations Research, INFORMS, vol. 63(1), pages 104-121, February.
    7. Josep J. Masdemont & Luis Ortiz-Gracia, 2014. "Haar wavelets-based approach for quantifying credit portfolio losses," Quantitative Finance, Taylor & Francis Journals, vol. 14(9), pages 1587-1595, September.
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    Cited by:

    1. Kirkby, J. Lars & Leitao, Álvaro & Nguyen, Duy, 2021. "Nonparametric density estimation and bandwidth selection with B-spline bases: A novel Galerkin method," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    2. Ahmed, Dilan & Soleymani, Fazlollah & Ullah, Malik Zaka & Hasan, Hataw, 2021. "Managing the risk based on entropic value-at-risk under a normal-Rayleigh distribution," Applied Mathematics and Computation, Elsevier, vol. 402(C).

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