1 Continuous Setting and Gaussian Generalized Lambda Distribution Model for Synthetic CDO Pricing

Pricing CDO has been a very challenging task to both researchers and practitioners. One of the major reasons was the complexity of CDO structure and the existence of skewness in correlation among tranches. Traditional approaches in pricing CDO include One-Factor-Gaussian-Copula model. However, such model has several drawbacks, for example, the only unknown is ρ- the correlation. However, for CDO, market prices of five tranches been quoted constantly and the implied ρ, which is the correlation that calculated from the market prices, is not a constant, which is called correlation smile. In order to more accurately pricing CDO, we need a model that can better capture the characteristics of such correlation smile. In our research, we propose a continuous Gaussian Generalized Lambda Distribution Model for synthetic CDO pricing (Gaussian GLD) to overcome the above issues. The con-tinuous setting comes from two aspects: Continuity of time and continuity of tranchlets. We model the common factor or systematic risk with normal distribution according to CAPM framework. Also, we model the idiosyncratic risk, for example, skewness and kurtosis, With generalized Lambda distribution (GLD). Due to the flexibility of GLD, which is described by a set of four parameters, the proposed model is partial distribution free and be able to replicate the market prices more accurately. 2