Importance Sampling in the Presence of PD-LGD Correlation

Adam Metzler and Alexandre Scott
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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

Risks, 2020, vol. 8, issue 1, 1-36

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.

Keywords: importance sampling; acceptance-rejection sampling; portfolio credit risk; tail probabilities; large deviation probabilities; stochastic recovery; PD-LGD correlation; credit risk; loss probabilities (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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