Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Importance sampling with splitting for portfolio credit risk

  • Received : 2019.09.20
  • Accepted : 2020.03.18
  • Published : 2020.05.31
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Abstract

We consider a credit portfolio with highly skewed exposures. In the portfolio, small number of obligors have very high exposures compared to the others. For the Bernoulli mixture model with highly skewed exposures, we propose a new importance sampling scheme to estimate the tail loss probability over a threshold and the corresponding expected shortfall. We stratify the sample space of the default events into two subsets. One consists of the events that the obligors with heavy exposures default simultaneously. We expect that typical tail loss events belong to the set. In our proposed scheme, the tail loss probability and the expected shortfall corresponding to this type of events are estimated by a conditional Monte Carlo, which results in variance reduction. We analyze the properties of the proposed scheme mathematically. In numerical study, the performance of the proposed scheme is compared with an existing importance sampling method.

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Acknowledgement

The author would like to thank the anonymous referees for their comments and suggestions on the first draft of this paper. Their valuable suggestions have greatly improve the representation of the paper.

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