A limit distribution of credit portfolio losses with low default probabilities

Xiaojun Shi, Qihe Tang, Zhongyi Yuan

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

This paper employs a multivariate extreme value theory (EVT) approach to study the limit distribution of the loss of a general credit portfolio with low default probabilities. A latent variable model is employed to quantify the credit portfolio loss, where both heavy tails and tail dependence of the latent variables are realized via a multivariate regular variation (MRV) structure. An approximation formula to implement our main result numerically is obtained. Intensive simulation experiments are conducted, showing that this approximation formula is accurate for relatively small default probabilities, and that our approach is superior to a copula-based approach in reducing model risk.

Original language English (US) 156-167 12 Insurance: Mathematics and Economics 73 https://doi.org/10.1016/j.insmatheco.2017.02.003 Published - Mar 1 2017

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Limit Distribution
Multivariate Regular Variation
Multivariate Extremes
Tail Dependence
Extreme Value Theory
Latent Variable Models
Heavy Tails
Copula
Latent Variables
Approximation
Simulation Experiment
Quantify
Credit
Default probability
Limit distribution
Model

All Science Journal Classification (ASJC) codes

• Statistics and Probability
• Economics and Econometrics
• Statistics, Probability and Uncertainty

Cite this

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A limit distribution of credit portfolio losses with low default probabilities. / Shi, Xiaojun; Tang, Qihe; Yuan, Zhongyi.

In: Insurance: Mathematics and Economics, Vol. 73, 01.03.2017, p. 156-167.

Research output: Contribution to journalArticle

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AB - This paper employs a multivariate extreme value theory (EVT) approach to study the limit distribution of the loss of a general credit portfolio with low default probabilities. A latent variable model is employed to quantify the credit portfolio loss, where both heavy tails and tail dependence of the latent variables are realized via a multivariate regular variation (MRV) structure. An approximation formula to implement our main result numerically is obtained. Intensive simulation experiments are conducted, showing that this approximation formula is accurate for relatively small default probabilities, and that our approach is superior to a copula-based approach in reducing model risk.

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