封閉偏斜常態因子模型違約風險估計之研究

投資組合的信用風險常使用常態關聯結構模型進行估計，但模型能調整的參數有限，本篇使用封閉常態關聯結構模型進行推導，其分配擁有常態分配的性質，也具有調整分配偏度及厚尾程度的參數，使其更適合用在解釋投資組合間的相依程度。在衡量投資組合的稀有事件時，其機率值不易模擬，但卻包含著高額資產違約時的重大損失，若僅使用蒙地卡羅法模擬其信用風險，其模擬耗費的時間比一般事件還久且變異較大，我們使用Glasserman and Li (Management Science, 51(11), 1643-1656, 2005)與Chiang et al. (Journal of Derivatives, 15(2), 8-19, 2007)各別提出的重要性取樣法(簡稱GIS法與MIS法)進行推導及延伸，在封閉偏斜常態關聯結構模型的投資組合下進行模擬，透過變異數縮減效果衡量兩種方法的模擬效率。數值結果顯示，在單因子模型中，MIS法所花費的時間較GIS法少，其變異數縮減效果顯著；在多因子模型中，GIS法能適用的範圍較廣，透過兩階段重要性取樣法，其變異數縮減效果良好，模擬時間也較蒙地卡羅法縮短。兩種方法都有其適用的模型，也具有良好的估計精準度及模擬穩定性。

關鍵字

信用違約風險；資產投資組合；常態關聯結構；封閉偏斜常態關聯結構；蒙地卡羅法；重要性取樣法；指數轉換；變異數縮減；直尋牛頓法

並列摘要

The credit risk of the portfolio is often estimated using the Normal Copula model, but the parameters that the model can adjust are limited. This paper uses the Closed Normal Copula model to derive. The CSN distribution has the nature of normal distribution, and also has the adjustment distribution skewness. The degree of parameters make it more suitable for interpreting the degree of dependency between portfolios. When measuring the rare events of a portfolio, the probability value is not easy to simulate, but it contains a large loss in the event of a high-value Asset Default. Using Monte Carlo to simulate its credit risk, the simulation takes longer than usual and varies greatly. We use the importance sampling method proposed by Glasserman and Li (Management Science, 51(11), 1643-1656, 2005) and Chiang et al. (Journal of Derivatives, 15(2), 8-19, 2007). Referred to as GIS method and MIS method, it is deduced and extended. The simulation is carried out under the portfolio of Closed Skew Normal Copula model, and the simulation efficiency of the two methods is measured by the reduction effect of variance. The numerical results show that in the single factor model, the MIS method takes less time than the GIS method, and the Variance Reduction effect is significant. In the multi-factor model, the GIS method can be applied to a wide range, through the two-stage importance sampling method. The Variance Reduction effect is good, and the simulation time is shortened compared with the Monte Carlo method. Both methods have their applicable models and also have good estimation accuracy and simulation stability.

並列關鍵字

Normal-Copula ； Closed-Skew-Normal-Copula ； Asset Portfolio ； Credit Default Risk ； Monte Carlo Method ； Importance Sampling ； Exponential Twisting ； Variation Reduction ； Line Search Newton method