One Factor Dynamic Model pricing and forecast of Synthetic CDOs

應用大樣本一致性資產組合(large homogeneous portfolio portfolio ; LHP)假設之單因子關聯結構模型(One Factor Copula Model)為以往評價合成型擔保債權憑證最廣為使用的方法。最早是由O’Kane and Schloegl (2001)所提出的應用LHP假設之單因子常態關聯結構模型，而其針對各分卷的評價結果僅有在權益分券(equity tranch)得到好的配適。Kalemanova et al. (2007) 提出應用LHP假設之單因子NIG關聯結構模型，其評價結果遠優於常態分配，但在中間順位(Mezzanine)層級以上的分券還是高估。以上的單因子模型皆是對2008年以前的擔保債權憑證做評價，且僅挑選特定幾天做分析，因此本文針對2008年三月到2013年三月做完整的長期分析，比較不同模型對於擔保債權憑證之評價結果。本文利用了單因子常態關聯結構模型、單因子NIG關聯結構模型以及單因子動態模型來做討論。在常態與NIG的單因子關聯結構模型中，最後實證結果分析顯示，期數n隨著時間遞減的話將能夠大幅改善評價結果；而在動態模型的部分，由於參數估計的方法不夠完善，因此得到的評價結果不符合預期。The most widely used methods used application of Large Homogeneous Portfolio (LHP) assumption of the one factor copula model for pricing synthetic CDOs. The one factor Gaussian copula model was first used by O'Kane and Schloegl (2001) proposed, however, only in equity tranches get a good evaluation of the results of the fit for each tranches. Kalemanova et al (2007) proposed the application of LHP assumption of one factor NIG copula model. The one factor copula model of NIG distribution evaluation results are far better than normal distribution, but overestimated above mezzanine tranches. The above models are all pricing of Synthetic CDOs before 2008, and select only certain days for analysis. Therefore, this paper in March 2008 to March 2013 to do a complete long-term analysis, comparison of different models for pricing of Synthetic CDOs results. In this paper, one factor Gaussian copula model, one factor NIG copula model and one factor dynamic model do discussion. In Gaussian and NIG one factor copula model, the empirical results of the final analysis, diminishing over time periods n, then will be able to significantly improve the results of Synthetic CDOs pricing. In the part of the one factor dynamic model, since the parameter estimation method is not perfect, so the results of Synthetic CDOs pricing are not in line with expectations