Abstract
We consider the problem of calculating tail loss probability and conditional excess for the Bernoulli mixture model of credit risk. This is an important problem as all credit risk models proposed in literature can be represented as Bernoulli mixture models. Thus, we deviate from the efficient simulation of credit risk literature in that we propose an efficient simulation algorithm for this general Bernoulli mixture model in contrast to previous works that focus on specific credit risk models like CreditRisk\(^+\) or Credit Metrics. The algorithm we propose is a combination of stratification, importance sampling based on cross-entropy, and inner replications using the geometric shortcut method. We evaluate the efficiency of our general method considering three different examples: CreditRisk\(^+\) and two of the latent variable models, the Gaussian and the t-copula model. Numerical results suggest that the proposed general algorithm is more efficient than the benchmark methods for these specific models.
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Acknowledgments
This work was supported by The Scientific and Technological Research Council of Turkey (TÜB\(\dot{\mathrm{I}}\)TAK) Research Fund Project 111M108 and Xi’an Jiaotong- Liverpool University Research Fund Project RDF-14-01-33, and partially supported by Boğaziçi Scientific Research Fund Project 6923.
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Başoğlu, İ., Hörmann, W. & Sak, H. Efficient simulations for a Bernoulli mixture model of portfolio credit risk. Ann Oper Res 260, 113–128 (2018). https://doi.org/10.1007/s10479-016-2241-1
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DOI: https://doi.org/10.1007/s10479-016-2241-1