Pricing Multiname Credit Derivatives: Heavy Tailed Hybrid Approach

Mashal, Roy; Naldi, Marco

doi:10.2139/ssrn.296402

Cited by 18 publications

(9 citation statements)

References 40 publications

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“…where the vector ) ( , ) , , ( The degrees of freedom of the copula can be estimated using a recursive procedure proposed by Mashal and Naldi (2001). Given the initial estimate…”

Section: Symmetric Student T-copulamentioning

confidence: 99%

Aggregation issues in operational risk

Giacometti¹,

Rachev²,

Chernobai³

et al. 2008

JOP

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In this paper we study copula-based models for aggregation of operational risk capital across business lines in a bank. A commonly used method of summation of the value-at-risk (VaR) measures, that relies on a hypothesis of full correlation of losses, becomes inappropriate in the presence of dependence between business lines and may lead to over-estimation of the capital charge. The problem can be further aggravated by the persistence of heavy tails in operational loss data; in some cases, the subadditivity property of value-at-risk may fail and the capital charge becomes underestimated. We use α-stable heavy-tailed distributions to model the loss data and then apply the copula approach in which the marginal distributions are consolidated in the symmetric and skewed Student tcopula framework. In our empirical study, we compare VaR and conditional VaR estimates with those obtained under the full correlation assumption. Our results demonstrate significant reduction in capital when a t-copula is employed. However, the capital reduction is significantly smaller than in cases where a moderately heavy-tailed or thin-tailed distribution is calibrated to loss data. We also show that for confidence levels below 94% VaR exhibits the super-additivity property.3

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“…where the vector ) ( , ) , , ( The degrees of freedom of the copula can be estimated using a recursive procedure proposed by Mashal and Naldi (2001). Given the initial estimate…”

Section: Symmetric Student T-copulamentioning

confidence: 99%

Aggregation issues in operational risk

Giacometti¹,

Rachev²,

Chernobai³

et al. 2008

JOP

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“…Duffie and Garleanu (2001) suggested dynamic intensities that are composed of the systematic and idiosyncratic intensities. Marshal and Naldi (2002) focused on heavy-tailed distributions with t-copulas. Kalemanova et al (2007) introduced the normal inverse Gaussian copula.…”

Section: Review Of Literaturementioning

confidence: 99%

A factor contagion model for portfolio credit derivatives

Choe

Jang

Kwon

2014

Quantitative Finance

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We propose a factor contagion model with the Marshall-Olkin copula for correlated default times and develop an analytic approach for finding the kth default time distribution based on our model. We combine a factor copula model with a contagion model under the assumption that the individual default intensities follow contagion processes, and that the default times have a dependence structure with the Marshall-Olkin copula. Then, we derive an analytic formula for the kth default time distribution and apply it to compute the price of portfolio credit derivatives, such as kth-to-default swaps and single-tranche CDOs. To test efficiency and accuracy of our formula, we compare the theoretical prediction with existing methods.

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“…The approach is further explored in Rogge and Scho¨nbucher (2003), where the copula set-up can actually be calibrated to jumps conditional on default. Further development of the copula approach has focused on Archimedean copulae, as in Scho¨nbucher (2002) and Rogge and Scho¨nbucher (2003), and on variations of the Gaussian copula, such as the t-copula (Mashal and Naldi, 2001) and the 'one-factor' Gaussian copula. The latter is described in more detail in Gregory and Laurent (2003a, b), Andersen et al (2003) and later on in Hull and White (2003).…”

Section: Portfolio Loss Distributionmentioning

confidence: 99%

Correlation at First Sight

Friend¹,

Rogge²

2005

Economic Notes

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The synthetic collateralized debt obligation (CDO) market has, over the last year, seen a significant increase in liquidity and transparency. The availability of published prices such as TracX and iBoxx tranches permits the calibration of model parameters, which was not achievable a year ago. This paper details what we believe has become the market standard approach in CDO valuation. The valuation model is introduced and analysed in depth to develop a better practical understanding of its use and the implications of parameter selection and calibration. In particular, we examine the idea that correlation within a copula model can be seen to be an equivalent measure to volatility in a standard B&S option framework and, correspondingly, we seek to calibrate smile and skew.(J.E.L.: G13).

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Pricing Multiname Credit Derivatives: Heavy Tailed Hybrid Approach

Cited by 18 publications

References 40 publications

Aggregation issues in operational risk

Aggregation issues in operational risk

A factor contagion model for portfolio credit derivatives

Correlation at First Sight

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