Applying importance sampling for estimating coherent credit risk contributions

Merino, Sandro; Nyfeler, Mark A

doi:10.1088/1469-7688/4/2/009

Cited by 20 publications

(20 citation statements)

References 6 publications

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“…With respect to the simulation algorithm, we run a competing test of both Monte Carlo estimation methods, standard and proposed, as in Merino and Nyfeler (2004) and Glasserman and Li (2005), among others. The comparison consists of the following: Given a portfolio, 50 estimates of η are obtained by means of each simulation algorithm.…”

Section: Resultsmentioning

confidence: 99%

“…Laeven and Goovaerts (2004) also consider conditional allocations, but their study does so with a different purpose, capital optimization, and does not integrate them to form an unconditional allocation vector. Merino and Nyfeler (2004) apply an importance sampling algorithm to the problem of calculating the ES allocation vector, which is different from defining a new allocation method that uses as input a vector derived from an efficient simulation algorithm for the aggregated capital, as happens with our approach.…”

Section: Discussionmentioning

confidence: 99%

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Linking the Problems of Estimating and Allocating Unconditional Capital

2014

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This paper addresses two problems related to determining the unconditional capital required by a credit portfolio: Estimating it using Monte Carlo simulation and allocating it among the different risk units that form the portfolio. By elaborating on a tractable analytical framework, we propose a new simulation algorithm and a new allocation method. Both contributions rely on the conditional loss distributions and share the same core idea. We discuss their optimality, consistence and practical advantages. In an empirical study based on American data, we show the remarkable gains in efficiency achieved by the former and the improvement in the standard variance-covariance allocation provided by the latter. Estimating it using Monte Carlo simulation and allocating it among the different risk units that form the portfolio. By elaborating on a tractable analytical framework, we propose a new simulation algorithm and a new allocation method. Both contributions rely on the conditional loss distributions and share the same core idea. We discuss their optimality, consistence and practical advantages. In an empirical study based on American data, we show the remarkable gains in efficiency achieved by the former and the improvement in the standard variance-covariance allocation provided by the latter.

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Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Linking the Problems of Estimating and Allocating Unconditional Capital

2014

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“…Inspired by that paper, and using results from Kang and Shahabuddin (2005) and Merino and Nyfeler (2004), I work out a three-stage IS algorithm for the hierarchical VCG model based on the exponential tilting of the systematic factors and conditional portfolio loss distribution.…”

Section: Importance Sampling Algorithmmentioning

confidence: 99%

A Hierarchical Model of Tail Dependent Asset Returns for Assessing Portfolio Credit Risk

Tente

2011

SSRN Journal

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This paper introduces a multivariate pure-jump Lévy process which allows for skewness and excess kurtosis of single asset returns and for asymptotic tail dependence in the multivariate setting. It is termed Variance Compound Gamma (VCG). The novelty of my approach is that, by applying a two-stage stochastic time change to Brownian motions, I derive a hierarchical structure with different properties of inter-and intra-sector dependence. I investigate the properties of the implied static copula families and come to the conclusion that they are ordered with respect to their parameters and that the lower-tail dependence of the intra-sector copula is increasing in the absolute values of skewness parameters. Furthermore, I show that the joint characteristic function of the VCG asset returns can be explicitly given as a nested Archimedean copula of their marginal characteristic functions. Applied to credit portfolio modelling, the framework introduced results in a more conservative tail risk assessment than a Gaussian framework with the same linear correlation structure, as I show in a simulation study. To foster the simulation efficiency, I provide an Importance Sampling algorithm for the VCG portfolio setting. Non-technical summaryIn this paper, I introduce a novel model of tail-dependent asset returns which can be used for the purposes of structural credit risk modelling. Similar to the copula approach proposed recently by Puzanova (2011), the Variance Compound Gamma (VCG) model presented here implies a hierarchical dependence structure with stronger dependence within pre-specified sectors than between them. The magnitude of sector-specific dependence parameters governing the tail dependence property can vary from one sector to another, allowing the model to cope with concentration risk. An advantage of the VCG framework over the aforementioned copula approach is its more general applicability, which is not limited to a static, one-period consideration of portfolio credit risk. In fact, the fundamental VCG model of asset returns can be utilised for financial modelling (pricing of financial derivatives etc.) whenever using multivariate jump-driven Lévy processes with a hierarchical dependence structure is deemed appropriate.Allowing jumps in the sample paths of the asset returns, the VCG model overcomes the shortcomings of a Gaussian/Brownian framework, such as anticipated default time, symmetric and mesokurtic probability distribution of the underlying and linear dependence structure. The jumps occur simultaneously for asset returns that are evaluated at a common business time. A business time common to all assets in an appropriately specified sector is a stochastic process which represents the irregular flow of information that is only relevant for that particular sector. The sector-specific business times themselves are evaluated at another common random time, which represents the flow of information that is relevant for the whole market, such as changes in the overall macroeconomic conditions. This two-s...

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“…Control variates are employed by Tchistiakov et al (2004) where the Vasicek distribution is considered as a control variable. Importance sampling (IS) is adopted by Kalkbrener et al (2004); Merino & Nyfeler (2005) for the calculation of Expected Shortfall Contribution and by Glasserman & Li (2005); Glasserman (2006) for the calculation of VaR and VaRC. We note that the difficulty with Monte Carlo simulation mainly concerns the determination of VaRC since the estimate expressed in formula (2) is based on the very rare event that portfolio loss L = VaR.…”

Section: Importance Samplingmentioning

confidence: 99%