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Importance Sampling in the Presence of PD-LGD Correlation

1
Department of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada
2
Department of Applied Mathematics, University of Western Ontario, London, ON N6A 3K7, Canada
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Author to whom correspondence should be addressed.
Risks 2020, 8(1), 25; https://doi.org/10.3390/risks8010025
Received: 20 January 2020 / Revised: 4 March 2020 / Accepted: 5 March 2020 / Published: 10 March 2020
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. View Full-Text
Keywords: importance sampling; acceptance-rejection sampling; portfolio credit risk; tail probabilities; large deviation probabilities; stochastic recovery; PD-LGD correlation; credit risk; loss probabilities importance sampling; acceptance-rejection sampling; portfolio credit risk; tail probabilities; large deviation probabilities; stochastic recovery; PD-LGD correlation; credit risk; loss probabilities
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Metzler, A.; Scott, A. Importance Sampling in the Presence of PD-LGD Correlation. Risks 2020, 8, 25.

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