Pricing CDO Based On The Gamma Process

CDO(Collateralized Debt Obligations) is a fixed incoming security whose portfolio contains one or diversity bonds .In fact it is a new method to merge the risk into another class of risk. First, the bank sells SPV the true portfolio ,according to the cash flow, the CDO can be divided into 3 class of tranches, senior tranche,mezzanine tranche,equity tranche,its aim is to sell different of risk to different taste of investor.The senior tranche should be AAA credit rating at least.The equity tranche usually absorbs the most part of risk,it also gives the highest pay off to the investor.The risk classification of mezzanine tranche lies between the senior and equity tranche,but the equity tranche does not have the risk classification.The common method of pricing the CDOs is the Gaussian One-factor Model, which implies that the correlation of each entity of portfolio is manipulated by a Gaussian factor. The model can give a semi-formula of loss distribution. According to the feedback of the market, this model has a fatal mistake, the essential of this phenomenon comes from the thin tail of Gaussian distribution. This article describes a new approach to price the CDO, the key point is the default incidents based on the Gamma process are independent, through the adjustment of parameters of Gamma process to overcome the correlation of default.This article's construction :first introduce the concept of CDO, analyst the problem of Gaussian copula method, then pricing CDO's risk premium of each tranche by intensity function and business time path which is sum of the Gamma process. At last, decide the tranche's attachment and detachment again to hedge the risk.