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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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    References listed on IDEAS

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    1. Michael B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.
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    Cited by:

    1. Dimitris Andriosopoulos & Michalis Doumpos & Panos M. Pardalos & Constantin Zopounidis, 2019. "Computational approaches and data analytics in financial services: A literature review," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(10), pages 1581-1599, October.
    2. İsmail Başoğlu & Wolfgang Hörmann & Halis Sak, 2018. "Efficient simulations for a Bernoulli mixture model of portfolio credit risk," Annals of Operations Research, Springer, vol. 260(1), pages 113-128, January.
    3. Sunggon Kim & Jisu Yu, 2023. "Stratified importance sampling for a Bernoulli mixture model of portfolio credit risk," Annals of Operations Research, Springer, vol. 322(2), pages 819-849, March.
    4. Hee-Geon Kang & Sunggon Kim, 2025. "An adaptive importance sampling for locally stable point processes," Computational Statistics, Springer, vol. 40(7), pages 3745-3779, September.
    5. 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.
    6. Kyriakos Georgiou & Athanasios N. Yannacopoulos, 2023. "Probability of Default modelling with L\'evy-driven Ornstein-Uhlenbeck processes and applications in credit risk under the IFRS 9," Papers 2309.12384, arXiv.org.

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