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Fast simulations in credit risk

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  • Halis Sak
  • Wolfgang Hörmann

Abstract

We consider the problem of simulating tail loss probabilities and expected losses conditioned on exceeding a large threshold (expected shortfall) for credit portfolios. Our new idea, called the geometric shortcut, allows an efficient simulation for the case of independent obligors. It is even possible to show that, when the average default probability tends to zero, its asymptotic efficiency is higher than that of the naive algorithm. The geometric shortcut is also useful for models with dependent obligors and can be used for dependence structures modeled with arbitrary copulae. The paper contains the details for simulating the risk of the normal copula credit risk model by combining outer importance sampling with the geometric shortcut. Numerical results show that the new method is efficient in assessing tail loss probabilities and expected shortfall for credit risk portfolios. The new method outperforms all known methods, especially for credit portfolios consisting of weakly correlated obligors and for evaluating the tail loss probabilities at many thresholds in a single simulation run.

Suggested Citation

  • Halis Sak & Wolfgang Hörmann, 2012. "Fast simulations in credit risk," Quantitative Finance, Taylor & Francis Journals, vol. 12(10), pages 1557-1569, October.
  • Handle: RePEc:taf:quantf:v:12:y:2012:i:10:p:1557-1569
    DOI: 10.1080/14697688.2011.564199
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    File URL: http://hdl.handle.net/10.1080/14697688.2011.564199
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    1. repec:spr:annopr:v:260:y:2018:i:1:d:10.1007_s10479-016-2241-1 is not listed on IDEAS
    2. Ferrer, Alex & Casals, José & Sotoca, Sonia, 2016. "Efficient estimation of unconditional capital by Monte Carlo simulation," Finance Research Letters, Elsevier, vol. 16(C), pages 75-84.

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