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This paper is dedicated to the risk analysis of credit portfolios. Assuming that default indicators form an exchangeable sequence of Bernoulli random variables and as a consequence of de Finetti’s theorem, default indicators are Binomial mixtures. We can characterize the supermodular order between two exchangeable Bernoulli random vectors in terms of the… (More)

- Jean-Paul Laurent, Areski Cousin, +20 authors Olivier Vigneron
- 2007

This contribution is an abridged version of the research paper “hedging default risks of CDOs in Markovian contagion models” (2008) to which we refer for further reading. We exhibit a replicating strategy of CDO tranches based upon dynamic trading of the corresponding credit default swap index. The aggregate loss follows a homogeneous Markov chain… (More)

- Areski Cousin, Elena Di Bernardino
- J. Multivariate Analysis
- 2013

In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk portfolio. The lower-orthant VaR is constructed from level sets of multivariate distribution functions whereas the… (More)

While the Gaussian copula model is commonly used as a static quotation device for CDO tranches, its use for hedging is questionable. In particular, the spread delta computed from the Gaussian copula model assumes constant base correlations, whereas we show that the correlations are dynamic and correlated to the index spread. It might therefore be expected… (More)

Service) collaborative project for which we are very grateful. The authors also thank Marek Rutkowski for useful discussions and comments.

- Tomasz R. Bielecki, Areski Cousin, Stéphane Crépey, Alexander Herbertsson
- J. Optimization Theory and Applications
- 2014

We consider a bottom-up Markovian copula model of portfolio credit risk where dependence among credit names mainly stems from the possibility of simultaneous defaults. Due to the Markovian copula nature of the model, calibration of marginals and dependence parameters can be performed separately using a two-steps procedure, much like in a standard static… (More)

This paper is dedicated to the risk analysis of credit portfolios. Assuming that default indicators form an exchangeable sequence of Bernoulli random variables and as a consequence of de Finetti’s theorem, default indicators are Binomial mixtures. We can characterize the supermodular order between two exchangeable Bernoulli random vectors in terms of the… (More)

- Salah Amraoui, Laurent Cousot, +14 authors Olivier Vigneron
- 2010

Up to the 2007 crisis, research within bottom-up CDO models mainly concentrated on the dependence between defaults. Since then, due to substantial increases in market prices of systemic credit risk protection, more attention has been paid to recovery rate assumptions. In this paper, we use stochastic orders theory to assess the impact of recovery on CDOs… (More)

In this paper, we prove that the conditional dependence structure of default times in the Markov model of [4] belongs to the class of Marshall-Olkin copulas. This allows us to derive a factor representation in terms of “common-shocks”, the latter beeing able to trigger simultaneous defaults in some pre-specified groups of obligors. This representation… (More)

This paper intends to provide insights about the topical issue of risk managing synthetic CDOs. We stand in the grey zone between mathematical finance and financial econometrics, between academic and market practitioners approaches. We chose to first present two scholar models, each of them leading to perfect replication of CDO tranches with credit default… (More)