2007) A Semi-Analytical Parametric Model for Dependant Defaults , working paper www.defaultrisk.com

A semi-analytical parametric approach to modeling default dependency is presented. It is a multi-factor model based on instantaneous default correlation that also takes into account higher order default correlations. It is capable of accommodating a term structure of default correlations and has a dynamic formulation in the form of a continuous time Markov chain. With two factors and a constant hazard rate, it provides perfect fits to four tranches of CDX.NA.IG and iTraxx Europe CDOs of 5, 7 and 10 year maturities. With time dependent hazard rates, it provides perfect fits to all the five tranches for all three maturities. Credit derivatives market has grown rapidly in recent years in response to the growing need for transferring and hedging credit risk. Growing innovations in this market has made understanding these products more urgent than ever. Various models have been developed to understand the role of default correlation on the prices of such products referencing a portfolio of underlying assets. A method for pricing these correlation products that has become standard is based on the Gaussian copula. There are some well known shortcomings in this approach. It deals effectively with default time correlation rather than default correlation itself. There is no straightforwar