The One-factor Copula Model and the Time Series Model for Synthetic CDO Pricing

• Main Authors: Liu, Shih Ching, 劉釋璟
• Other Authors: 劉惠美
• Format: Others
• Language: zh-TW
• Online Access: http://ndltd.ncl.edu.tw/handle/50805082434077998246

碩士 === 國立政治大學 === 統計研究所 === 103 === 　　Lamb, Perraudin, Landschoot (2009) proposed the one-factor copula model with the common factor under the assumption of AR(p) for pricing synthetic CDO. Their best model was the mixture model with AR(1). Additionally, there were good fits on different tranches, except the equity tranch. This paper applies the one-factor Gaussian copula model with the common factor under the assumption of AR(1) to the pricing of CDX.NA.IG. Series 9 weekly data (5-year maturity). We minimize the total absolute error on different tranches to obtain the parameters of different models. We compare three sets of models: (1) The one-factor Gaussian copula model (fixed maturity) v.s. the one-factor NIG copula model (fixed maturity). (2) The one-factor Gaussian copula model (declined maturity) v.s. the one-factor NIG copula model (declined maturity). (3) The one-factor Gaussian copula model (fixed maturity) v.s. the one-factor NIG copula model (fixed maturity) v.s. the one-factor Gaussian copula model with the common factor under the assumption of AR(1). In the one-factor Gaussian copula model with the common factor under the assumption of AR(1), we find the correlation parameter is stable through the observed period, ranging from 0.7 to 0.9. The same fact was observed in Lamb et al.,2009. This means that the market spreads are driven considerably by the level of one factor lag, not the default correlations.