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Importance Sampling in the Presence of PD-LGD Correlation

Author

Listed:
  • Adam Metzler

    (Department of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada)

  • Alexandre Scott

    (Department of Applied Mathematics, University of Western Ontario, London, ON N6A 3K7, Canada)

Abstract

This paper seeks to identify computationally efficient importance sampling (IS) algorithms for estimating large deviation probabilities for the loss on a portfolio of loans. Related literature typically assumes that realised losses on defaulted loans can be predicted with certainty, i.e., that loss given default (LGD) is non-random. In practice, however, LGD is impossible to predict and tends to be positively correlated with the default rate and the latter phenomenon is typically referred to as PD-LGD correlation (here PD refers to probability of default, which is often used synonymously with default rate). There is a large literature on modelling stochastic LGD and PD-LGD correlation, but there is a dearth of literature on using importance sampling to estimate large deviation probabilities in those models. Numerical evidence indicates that the proposed algorithms are extremely effective at reducing the computational burden associated with obtaining accurate estimates of large deviation probabilities across a wide variety of PD-LGD correlation models that have been proposed in the literature.

Suggested Citation

  • Adam Metzler & Alexandre Scott, 2020. "Importance Sampling in the Presence of PD-LGD Correlation," Risks, MDPI, vol. 8(1), pages 1-36, March.
  • Handle: RePEc:gam:jrisks:v:8:y:2020:i:1:p:25-:d:330917
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    References listed on IDEAS

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    1. repec:czx:journl:v:18:y:2011:i:28:id:183 is not listed on IDEAS
    2. Scott, Alexandre & Metzler, Adam, 2015. "A general importance sampling algorithm for estimating portfolio loss probabilities in linear factor models," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 279-293.
    3. Shaojie Deng & Kay Giesecke & Tze Leung Lai, 2012. "Sequential Importance Sampling and Resampling for Dynamic Portfolio Credit Risk," Operations Research, INFORMS, vol. 60(1), pages 78-91, February.
    4. Chan, Joshua C.C. & Kroese, Dirk P., 2010. "Efficient estimation of large portfolio loss probabilities in t-copula models," European Journal of Operational Research, Elsevier, vol. 205(2), pages 361-367, September.
    5. Paul Glasserman & Jingyi Li, 2005. "Importance Sampling for Portfolio Credit Risk," Management Science, INFORMS, vol. 51(11), pages 1643-1656, November.
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    Cited by:

    1. Christoph Frei, 2020. "A New Approach to Risk Attribution and Its Application in Credit Risk Analysis," Risks, MDPI, vol. 8(2), pages 1-13, June.

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