PRICING AND HEDGING CDOs WITH LÉVY BASE CORRELATION

Abstract

We consider a collateralized debt obligation (CDO) with standard credit default swap (CDS) indices as the reference portfolio. Such a CDO is referred to as synthetic CDO, and it is designed to transfer the credit risk on a reference portfolio of assets between parties. CDOs have recently become very popular credit instruments. A standard feature of a CDO structure is the tranching of credit risk, i.e., creating multiple tranches of securities which have varying degrees of seniority and risk exposure: the equity tranche is the first to be affected by losses in the event of one or more defaults in the portfo-lio. If losses exceed the value of this tranche, they are absorbed by the mezzanine tranche(s). Losses that have not been absorbed by the other tranches are sustained by the senior tranche and finally by the super-senior tranche. In such a way, each tranche protects the ones senior to it from the risk of loss on the underlying portfolio. The CDO investors take on exposure to a particular tranche, effectively selling credit protection to the CDO issuer, and in turn collecting premiums (spreads). Tranche spreads are daily quoted in the market. To price a synthetic CDO, one needs a model that captures the dependency structure in the un-derlying portfolio and gives a good fit to the market prices of different tranches simultaneously