Modelling Dependence for Credit Derivatives with Copulas

Jouanin, Jean-Frédéric; Rapuch, Grégory; Riboulet, Gaël; Roncalli, Thierry

doi:10.2139/ssrn.1032561

Cited by 20 publications

(7 citation statements)

References 19 publications

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“…This is assumed in order to simplify the parameterization of the model and to focus on default correlation rather than spread correlation, but the assumption can be removed if one is willing to complicate the parameterization of the model. In general, when stochastic intensities follow diffusion processes, spread correlation is of second order with respect to default correlation in most cases, as it has been recognized in Jouanin et al (2001), for example. We also define the integrated quantities …”

Section: Numerical Simulationsmentioning

confidence: 94%

Arbitrage‐free Bilateral Counterparty Risk Valuation Under Collateralization and Application to Credit Default Swaps

Brigo

Capponi²,

Pallavicini³

2012

Mathematical Finance

151

121

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We develop an arbitrage‐free valuation framework for bilateral counterparty risk, where collateral is included with possible rehypothecation. We show that the adjustment is given by the sum of two option payoff terms, where each term depends on the netted exposure, i.e., the difference between the on‐default exposure and the predefault collateral account. We then specialize our analysis to credit default swaps (CDS) as underlying portfolios, and construct a numerical scheme to evaluate the adjustment under a doubly stochastic default framework. In particular, we show that for CDS contracts a perfect collateralization cannot be achieved, even under continuous collateralization, if the reference entity’s and counterparty’s default times are dependent. The impact of rehypothecation, collateral margining frequency, and default correlation‐induced contagion is illustrated with numerical examples.

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Section: Numerical Simulationsmentioning

confidence: 94%

Arbitrage‐free Bilateral Counterparty Risk Valuation Under Collateralization and Application to Credit Default Swaps

Brigo

Capponi²,

Pallavicini³

2012

Mathematical Finance

151

121

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“…By Fubini's theorem, the copulas defined by (9) are the same as the copulas associated with the periodic functionsc = c α and defined by (2). We thus have, by (2) and using periodicity of c (thus replacing c(·) by c(·−1), which is helpful in some computational respects):…”

Section: A Smooth Family That Reachesmentioning

confidence: 99%

New Families of Copulas Based on Periodic Functions

Alfonsi

Brigo²

2005

Comm. in Stats. - Theory & Methods

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Although there exists a large variety of copula functions, only a few are practically manageable, and often the choice in dependence modeling falls on the Gaussian copula. Further, most copulas are exchangeable, thus implying symmetric dependence. We introduce a way to construct copulas based on periodic functions. We study the two-dimensional case based on one dependence parameter and then provide a way to extend the construction to the n-dimensional framework. We can thus construct families of copulas in dimension n and parameterized by n − 1 parameters, implying possibly asymmetric relations. Such "periodic" copulas can be simulated easily.

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“…25 • Pricing the default contingent instrument. For example pricing first-to-default takes 16 seconds.…”

Section: Computational Effortmentioning

confidence: 99%

“…24 All the following results were measured with Matlab on a standard PC 700 MHz and 128MB RAM, for 100,000 simulation trials, 5 names, and 3 years horizon. 25 With three months piecewise flat hazard rate marginals for default. 26 Specifically, since defaults are tail events, importance sampling would be very effective, especially for baskets with few high grade names.…”

Section: Pricing Examplesmentioning

confidence: 99%