Inria / Raweb 2004
Team: Mathfi

Search in Activity Report, year 2004:


Team : mathfi

Section: New Results

Keywords: credit derivatives, Marshall-Olkin copula.

Credit risk

Participants: B. Jottreau, Y. Elouerkhaoui.

Modelisation of credit default risk has been one of the main themes of the weekly seminar in the University of Marne la Vallée. B. Jottreau has started a thesis on this subject. The next release for Premia, Premia8, will include algorithms for pricing credit risk derivatives.

Y. Elouerkhaoui has continued to work on the valuation and hedging of basket credit derivatives in the Marshall-Olkin copula framework. The two main research themes are: the modelling of default correlation in the context of credit derivatives pricing, and the study of correlation market incompleteness and hedging.

Local risk minimization hedging in multi-credit markets

We have tackled the issue of hedging basket default swaps with their underlying single-name instruments. The payoff of basket products such as first-to-default swaps and CDOs is dependent on the multivariate default behaviour of the underlying credits. Clearly, default correlation risk introduces a market incompleteness, which cannot be hedged with plain vanilla instruments. To handle market incompleteness, we have used a local-risk minimization approach. We have highlighted the various components of the credit-hedging problem: spread risk, default risk and carry; and we have developed hedging strategies corresponding to the minimization of each type of risk. [35]

Modelling of default correlation in complex credit derivatives

We have studied default correlation risk in a new generation of basket products, known as CDOs of CDOs (or CDO squared) and baskets of baskets. The valuation of these products depends on a compounded type of default correlation risk. Similarly to compound options, which depend on "volatility of volatility", the value of CDOs of CDOs depends on the marginal loss distributions of each underlying CDO and their joint dependence, which is referred to as "correlation of correlation". To analyse this type of risk, we have developed the "Equivalent Single-Name Process" approximation, where the characterization of basket securities is simplified and their joint dependence is analytically tractable. We have considered each basket security in the underlying portfolio as a single-name security whose default time is driven by a Poisson process, and we have derived the properties of this process in the MO model. We have used a technique similar to our "Homogeneous Portfolio" approximation. [33]