A general importance sampling algorithm for estimating portfolio loss probabilities in linear factor models

This paper develops a novel importance sampling algorithm for estimating the probability of large portfolio losses in the conditional independence framework. We apply exponential tilts to (i) the distribution of the natural sufficient statistics of the systematic risk factors and (ii) conditional de...

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Vydáno v:Insurance, mathematics & economics Ročník 64; s. 279 - 293
Hlavní autoři: Scott, Alexandre, Metzler, Adam
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 01.09.2015
Elsevier Sequoia S.A
Témata:
[formula omitted] copula
Algorithms
Copulas
Cross-entropy method
Exponential tilts
Gaussian copula
Importance sampling
Kullback–Leibler divergence
Mathematical models
Monte Carlo
Parameter estimation
Portfolio loss
Portfolio performance
Portfolios
Probability
Risk factors
Sampling
Statistics
Studies
Values
Kullback–Leibler divergence
t copula
Monte Carlo
Cross-entropy method
Portfolio loss
Gaussian copula
Importance sampling
Exponential tilts
ISSN:0167-6687, 1873-5959
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Abstract This paper develops a novel importance sampling algorithm for estimating the probability of large portfolio losses in the conditional independence framework. We apply exponential tilts to (i) the distribution of the natural sufficient statistics of the systematic risk factors and (ii) conditional default probabilities, given the simulated values of the systematic risk factors, and select parameter values by minimizing the Kullback–Leibler divergence of the resulting parametric family from the ideal (zero-variance) importance density. Optimal parameter values are shown to satisfy intuitive moment-matching conditions, and the asymptotic behaviour of large portfolios is used to approximate the requisite moments. In a sense we generalize the algorithm of Glasserman and Li (2005) so that it can be applied in a wider variety of models. We show how to implement our algorithm in the t copula model and compare its performance there to the algorithm developed by Chan and Kroese (2010). We find that our algorithm requires substantially less computational time (especially for large portfolios) but is slightly less accurate. Our algorithm can also be used to estimate more general risk measures, such as conditional tail expectations, whereas Chan and Kroese (2010) is specifically designed to estimate loss probabilities.
AbstractList This paper develops a novel importance sampling algorithm for estimating the probability of large portfolio losses in the conditional independence framework. We apply exponential tilts to (i) the distribution of the natural sufficient statistics of the systematic risk factors and (ii) conditional default probabilities, given the simulated values of the systematic risk factors, and select parameter values by minimizing the Kullback-Leibler divergence of the resulting parametric family from the ideal (zero-variance) importance density. Optimal parameter values are shown to satisfy intuitive moment-matching conditions, and the asymptotic behaviour of large portfolios is used to approximate the requisite moments. In a sense we generalize the algorithm of Glasserman and Li (2005) so that it can be applied in a wider variety of models. We show how to implement our algorithm in the t copula model and compare its performance there to the algorithm developed by Chan and Kroese (2010). We find that our algorithm requires substantially less computational time (especially for large portfolios) but is slightly less accurate. Our algorithm can also be used to estimate more general risk measures, such as conditional tail expectations, whereas Chan and Kroese (2010) is specifically designed to estimate loss probabilities.
Author Metzler, Adam
Scott, Alexandre
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Cites_doi 10.1016/S1042-9573(03)00040-8
10.1016/j.ejor.2010.01.003
10.1287/opre.1060.0367
10.1287/mnsc.1050.0415
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Keywords Kullback–Leibler divergence
t copula
Monte Carlo
Cross-entropy method
Portfolio loss
Gaussian copula
Importance sampling
Exponential tilts
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Asmussen, Glynn (br000005) 2007
Bickel, Doksum (br000010) 2001
Hu, Fu, Marcus (br000030) 2007; 55
Gordy (br000025) 2003; 12
Merino, Nyfeler (br000035) 2002; 15
Chan, Kroese (br000015) 2010; 205
Chan (10.1016/j.insmatheco.2015.06.001_br000015) 2010; 205
Gordy (10.1016/j.insmatheco.2015.06.001_br000025) 2003; 12
Glasserman (10.1016/j.insmatheco.2015.06.001_br000020) 2005; 51
Hu (10.1016/j.insmatheco.2015.06.001_br000030) 2007; 55
Bickel (10.1016/j.insmatheco.2015.06.001_br000010) 2001
Merino (10.1016/j.insmatheco.2015.06.001_br000035) 2002; 15
Asmussen (10.1016/j.insmatheco.2015.06.001_br000005) 2007
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SubjectTerms [formula omitted] copula
Algorithms
Copulas
Cross-entropy method
Exponential tilts
Gaussian copula
Importance sampling
Kullback–Leibler divergence
Mathematical models
Monte Carlo
Parameter estimation
Portfolio loss
Portfolio performance
Portfolios
Probability
Risk factors
Sampling
Statistics
Studies
Values
Title A general importance sampling algorithm for estimating portfolio loss probabilities in linear factor models
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