依據之前的文獻研究，市場上主要是在LHP (Large Homogeneous Portfolio) 假設下利用單因子常態關聯結構模式(One factor double Gaussian copula model) 評價擔保債權憑證 (Collateralized debt obligation, CDO)。但這會造成擔保債權憑證的評價與市場報價的差距過大，且會造成base correlation偏斜的情況。Kalemanova et al. (2007) 提出用Normal inverse Gaussian (NIG) 取代常態分配評價擔保債權憑證，此模型不但計算快速而且可以準確估計權益分券 (equity tranche) 的價格，但是它也過於高估了其它的分券的價格。 在本文中使用多變量封閉常態分配(Closed skew normal, 簡稱CSN) 分配取代NIG分配作擔保債權憑證分券的評價，CSN分配具有常態分配的性質，其線性組合仍具有封閉性的特質，且具有較多的參數以控制分配的偏態與峰態。但是與單因子常態關聯結構模式相同，多變量封閉常態分配的單因子關聯結構模式仍然無法估計的很準確，僅有在最高等級分券(senior tranche)的評價上有明顯的改進。 因此在本文中我們使用NIG與CSN複合分配之單因子關聯結構模式評價擔保債權憑證分券，在實例分析時得到極佳的評價結果，並且比單因子常態關聯結構模型具有更多的的參數以使模型更符合實際的需求。 / This article extends the Large Homogeneous Portfolio (LHP) and one factor double Gaussian copula approach for pricing CDOs. In the literature, the one factor double Gaussian copula model under LHP assumption fails to fit the prices of CDO tranches, moreover, it leads to the implied base correlation skew. Some researchers proposed using one factor double NIG copula model to price CDO tranches. It not only economizes on time but also fits the equity tranches exactly, but NIG models do not price other tranches well simultaneously. On the other hand, we substitute the NIG distribution with the Closed Skew normal (CSN) distribution. This family also has properties similar to the normal distribution, which is closure under convolution, and has extra parameters to control the shape. By using this model we get a better fit in the senior tranches, but it seriously overprices subordinate tranches. Thus we consider a mixture distribution of NIG and CSN distributions. The employments of this mixture distribution are comparatively well, and furthermore it brings more flexibility to the dependence structure.

本文採民國94、96、98、100、102年的台灣 「人力運用調查」 資料庫, 以關聯結構法找出組合誤差間的關聯結構密度函數與聯合機率密度函數, 建構隨機邊界關聯結構模型, 解決勞動市場上樣本選擇性問題。 之後分別針對男性及女性估計薪資方程式, 探討每位勞工的薪資效率程度。 本文男、 女性的勞工各按年齡、 工作經驗、 職業、 行業、 教育程度、 公司規模、 工作身分、 婚姻狀態、 工作地分為9大類, 在各類中分群比較薪資效率。 實證結果顯示, 公司規模、 工作身分、 工作地等 3 類, 不論有無考慮樣本選擇, 同一性別中的薪資效率變動趨勢大致一致, 但其餘 6 類, 有考慮樣本選擇的薪資效率變動明顯不同於未考慮樣本選擇。 在考慮了樣本選擇之後的實證結果大多打破以往文獻的預期, 可能是因為過往文獻探討薪資效率時, 大多未考慮樣本選擇, 即將無工作者樣本完全排除, 導致迴歸分析結果僅適用於有工作者。 除了探討薪資效率外, 本文也嘗試在隨機邊界法的架構下, 提出一個衡量性別歧視的新觀點, 將兩性薪資無效率的差異視為一種性別歧視。 若以新觀點衡量台灣的勞動市場, 會發現這5個年度中, 薪資差異幾乎可以完全歸諸於性別歧視。 這顯示即使兩性的薪資差異雖然逐年縮小, 但性別的刻板印象仍存於當今的台灣勞動市場, 造成明顯的性別歧視。 / This paper adopts the "Manpower Utilization Survey" data, a database conducted by Directorate General of Budget, Accounting & Statistics, Executive Yuan, ROC (DGBAS), to study the issues of gender wage differentials and underpayment. The econometric model considers sample selection under the framework of the stochastic frontier model with copula methods. It requires to correct for sample selection and derive the copula density function and joint probability density function by copula method. We separately estimate the male and female wage equations, respectively, to evaluate the wage efficiency and decompose the average wage differential between male and female into several components. The paper distinguishes workers into 9 categories, including age, experience, occupation, industry, education, firm size, working identity, marital status and working area, and compares the wage efficiency between those categories. The empirical results shows that, the trend of wage efficiency in the categories of firm size, working identity, and working area are almost the same in each gender whether correcting for the sample selection bias or not. However, in the remaining 6 categories, the wage efficiency changes substantially after correcting the sample selection bias. With the correction of the sample election bias, most of the findings differ from those from the past literatures. This may be attributed to the fact that the past works mainly focus on employed workers and lead to possible sample selection bias. The paper also tries to offer a new method to measure the gender discrimination, which considers the difference in wage inefficiency between the male-female inefficiency as an element of discrimination. The paper finds that the wage differential between male and female can explain almost the entire discrimination. This findings confirms that the gender discrimination still exists in the Taiwan’s labor market eventhough the wage differential between male and female decreases over time.

蒙地卡羅模擬是在組合信用風險的管理上相當實用的計算工具。衡量組合信用風險時，必須以適當的模型描述資產間的相依性。常態關聯結構是目前最廣為使用的模型，但實證研究認為 t 關聯結構更適合用於配適金融市場的資料。在本文中，我們採用 Bassamboo et al. (2008) 提出的極值相依模型建立 t 關聯結構用以捕捉資產之間的相關性。同時，為增進蒙地卡羅法之收斂速度，我們以 Chiang et al. (2007) 的重要性取樣法為基礎，將其拓展到極值相依模型下，並提出兩階段的重要性取樣技巧確保使用此方法估計一籃子信用違約時，所有模擬路徑均會發生信用事件。數值結果顯示，所提出的演算法皆達變異數縮減。而在模型自由度較低或是資產池較大的情況下，兩階段的重要性取樣法將會有更佳的估計效率。我們也以同樣的思路，提出用以估計投資組合損失機率的演算法。雖然所提出的演算法經過重要性取樣的技巧後仍無法使得欲估計的事件在所有模擬路徑下都會發生，但數值結果仍顯示所提出的方法估計效率遠遠優於傳統蒙地卡羅法。 / Monte Carlo simulation is a useful tool on portfolio credit risk management. When measuring portfolio credit risk, one should choose an appropriate model to characterize the dependence among all assets. Normal copula is the most widely used mechanism to capture this dependence structure, however, some emperical studies suggest that $t$-copula provides a better fit to market data than normal copula does. In this article, we use extremal depence model proposed by Bassamboo et al. (2008) to construct $t$-copula. We also extend the importance sampling (IS) procedure proposed by Chiang et al. (2007) to evaluate basket credit default swaps (BDS) with extremal dependence and introduce a two-step IS algorithm which ensures credit events always take place for every simulation path. Numerical results show that the proposed methods achieve variance reduction. If the model has lower degree of freedom, or the portfolio size is larger, the two-step IS method is more efficient. Following the same idea, we also propose algorithms to estimate the probability of portfolio losses. Althought the desired events may not occur for some simulations, even if the IS technique is applied, numerical results still show that the proposed method is much better than crude Monte Carlo.

綜觀國內外探討金融產業經營效率之相關文獻，多數針對銀行、證券、保險中其一產業進行獨立實證研究，較無法將金融控股之綜效表現加以捕捉並體現在估計效率值中，也因此在本文中，將同時涵蓋銀行業務與證券業務，並以納入金控體制與否加以區分為不同子集合進行探討，透過數理方法聯結金控體制下銀行與證券業務部門兩者間因多角化經營所產生之綜效，以修正傳統方法上表現綜效法上之不足，使估計效率值具有更高的參考依據。 此外，研究產業效率所參考之研究方法，在相關文獻中無參數法乃以資料包絡分析法(Data envelopement analysis, DEA)為多數研究者所採用；參數法則以隨機邊界模型(stochastic frontier approach, SFA)為主要研究方法，進一步在不同群組技術效率之比較中，Battese et al. (2004) 與 O’Donnell et al. (2008)提出為多數研究者所接受之共同邊界模型(Metafrontier)，而Huang et al. (2013)所提出之修正模型使共同邊界模型在效率研究上更加完備，本文則希望以此修正模型作為主要研究模型，並同時引用Battese et al. (2004)傳統模型加以比較：(1)考慮綜效前後 (2)傳統模型與修正模型間效率值的差異，期待為後續相關研究者在方法論上提供參考依據。 關鍵字：經營效率、技術效率、共同邊界、計量方法、關聯結構法、金融控股銀行 / This study aims to discuss the evidence suggested that synergy improve the operating performance of Taiwan’s commerical banks and securites firms. Furthermore, efficiency comparisons amongst two basis metafrontier models, Haung et al.(2013) and Battese et al.(2004), and copula-adjusted metafrontier. The empirical results suggest that copula-adjusted metafrontier could significantly improve the efficiency of financial holding companies based on the data of sample period 2001-2012. On the framework of copula-adjusted metafrontier, the evidence also imply that financial holging companysubsidiary technical efficiency is better than non-financial holding company compared to the framework of Haung et al.(2013) and Battese et al.(2004), the conclusion emphasis that synergy is perhaps one crucial key factor influenced the efficiency estimation. Otherwise, this study appears to support the copula-adjusted metafrontier model is also well-adjusted compared to programming techniques because not only it enables the statistical inferences to be drawn, but also provides more efficiency estimations.