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- Areski Cousin, Jean-Paul Laurent, M Denuit, R Elkamhi, M Jeanblanc, C Lefèvre +5 others
- 2008

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, Jean-David Fermanian, Salah Amraoui, Matthias Arnsdorf, Fahd Belfatmi +20 others
- 2007

Il s'agit d'une version concise de l'article " hedging default risks of CDOs in Markovian contation models " (2008) auquel nous renvoyons pour plus de dtails. Nous mettons enévidence une stratégie de duplication de tranches de CDO faisant appel au contrat de swap de défaut sur l'indice sous-jacent. La perte agrégée suit une chaˆıne de Markov. L'intensité de… (More)

We devise a bottom-up dynamic model of portfolio credit risk where instantaneous contagion is represented by the possibility of simultaneous defaults. Due to a 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 copula setup. In this… (More)

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)

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)

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

We consider a bottom-up Markovian copula model of portfolio credit risk where instantaneous contagion is possible in the form 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 copula setup. In… (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)

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)

In [5], the authors introduced a Markov copula model of portfolio credit risk where pricing and hedging can be done in a sound theoretical and practical way. Further theoretical backgrounds and practical details are developped in [6] and [7] where numerical illustrations assumed deterministic intensities and constant recoveries. In the present paper, we… (More)