信用連結債券的價值主要取決於所連結資產池內的資產違約情況，因此過去有許多文獻在評價時會利用Copula模擬各資產的違約時點，或是用Factor Copula估算他們在各時點下的違約機率。而本研究以Gaussian Factor Copula模型為主軸，對資產池違約機率做估計，以得到連結該資產池的信用連結債券價值。但過去文獻較常以給定參數的方式進行評價，本研究進一步利用市場實際資料估出模型參數並加入產業因子，以期達到符合市場的效果。 本研究利用已知的違約資訊對照模型結果，發現在給定原油價格成長率、產業GDP成長率及CAPM殘差之後，使用Factor Copula模型在資產池小且違約比例過高時容易低估損失，主要原因在於各資產的違約機率並非逼近1。且模型算出的預期損失會隨著距今時間變長而增加，但若資產池實際上沒有更多違約公司，模型的結果就可能會高估損失。而所有的變數又以參考價差對該商品價值的影響最大，因參考價差的數值取決於該公司的信用評等，因此可知信用連結債券價值主要還是與各公司信評有最大相關。 / The value of credit linked notes depends on whether the reference entities in the linked asset pool default or not, so some previous studies used Copula model to simulate the times to default or Factor Copula model to get the default probability. In this paper, with the Gaussian Factor Copula model adopted and industry factors taken into account, the default probability is estimated in order to obtain the value of the credit linked notes. Then, unlike other previous studies using the given parameters, this paper evaluated the parameters by using the model as well as market data, hoping to achieve the goal that results can reflect the real market situation. With real default information compared with the modeling results, three findings can be drawn given the growth rate of oil price, the growth rate of industrial GDP and the residuals of CAPM. First, the loss will be underestimated if the asset pool is small and the default proportion is too high mainly because not all the default probability approximates one. Second, expected default probability will be directly proportional to the time period between the present and the expected moment. So if there are not so many defaulting companies, then the loss might be overestimated. Last, the reference spread has the most impact on the product value among all the variables, and as we know, the reference spread of a company depends on its credit rating. Therefore, compared with other factors, credit rating remains the most essential to credit linked notes.

本論文在Li(2000)的Gaussian Copula的背景之下，將資產價值服從常態分配的假設改為服從Variance Gamma分配，利用Copula模型模擬債權群組內各個標的資產的違約時點，並利用蒙地卡羅抽取亂數的方法，取平均之後求得信用連結債券所連結的資產債權組合價值。除此之外，本論文比較假設資產價值服從常態分配、Student t分配和Variance Gamma分配下，計算求得的資產池價值。實證結果顯示，假設服從Variance Gamma分配最接近市場的真實違約資料。這是由於Variance Gamma分配具備Student t分配的厚尾性質，能有效捕捉常態分配缺少的尾端損失機率，並可調整偏態係數和峰態係數，可以求出更接近市場價值的評價結果。最後，在敏感度分析方面，改變影響資產池價值的兩大因子：平均違約回收率和資產間相關係數。結果顯示，當平均違約回收率高於0.7時，相關係數越高的債權群組，其資產池價值亦越高。若平均違約回收率越低且資產間相關係數越高的話，越容易出現一起違約的現象，因此資產池價值會下降。因此投資人在挑選信用連結債券時，應注意所連結的標的資產群組內資產報酬的相關性，最好避免相關性高的資產群組，以免金融海嘯來臨的時候，多個資產同時違約的情形發生。

許多新興風險隨著金融市場的變化而產生，以致於發生許多大型金融災害造成許多金融產業蒙受鉅額損失。而於金融市場尋求利潤已是金融產業重要的一環，有鑑於此，本論文提出ㄧ套完整的資產配置流程，利用技術指標建構綜合信號指標作為市場指標再選擇投資資產並估計、模擬、最適化投資權重並投資，以達到規避大型金融事件風險並獲取超額利潤。本論文亦嘗試不同股票評分指標、股票資產模型、結構模型、投資組合大小等組合，以找出最適合台灣股票支股票評分指標、資產模型以及投資組合大小。 本論文發現綜合信號指標作為市場指標可有效判讀金融事件的發生與結束時間，經由此指標判斷可獲得相當的超額利潤。本論文亦發現當投資組合為5支股票、資產模型為GJR GARCH(1,1)模型、相關結構型態為多元高斯Copula時可獲得超額利潤。

It is of great importance to find an analytical copula that will represent the empirical lower tail dependence. In this study, the pairwise empirical copula are estimated using data of the S&P 500 stocks during the period 2007-2010.Different optimization methods and measures of dependence have been used to fit Gaussian, t and Clayton copula to the empirical copulas, in order to represent the empirical lower tail dependence. These different measures of dependence and optimization methods with their restrictions, point at different analytical copulas being optimal. In this study the t copula with 5 degrees of freedom is giving the most fulfilling result, when it comes to representing lower tail dependence. The t copula with 5 degrees of freedom gives the best representation of empirical lower tail dependence, whether one uses the 'Empirical maximum likelihood estimator', or 'Equal Ƭ' as an approach.

Non-standard features such as copula deletion have long been dismissed as learner errors or were interpreted as results of simplification processes in English as a Lingua Franca (ELF), and only recent publications tend to acknowledge the influence of language contact in ELF settings (cf. Schneider 2012). The present paper analyses tokens of copula deletion in the Asian Corpus of English (ACE 2014) with respect to speaker L1s, situational context and syntactic environment, with our results suggesting a correlation between copula usage patterns in the speakers’ L1s and constructions involving copula deletion found in ACE. Thus, opening up the field to ELF settings, our data confirm findings of previous studies such as Sharma (2009) that point to contact-induced copula usage in non-standard English(es).

The three-factor model of Fama and French has proved to be a seminal contribution to asset pricing theory, and was recently extended to include two more factors, yielding the Fama-French five-factor model. Other proposed augmentations of the three-factor model includes the introduction of a momentum factor by Carthart. The extensive use of such factors in asset pricing theory and investing motivates the study of the distributional properties of the returns of these factors. However, previous studies have focused on subsets of these six factors on the U.S. market. In this thesis, the distributional properties of daily log-returns of the five Fama-French factors and the Carthart momentum factor in European data from 2009 to 2019 are examined. The univariate distributional dynamics of the factor log-returns are modelled as ARMA-NGARCH processes with skewed t distributed driving noise sequences. The Gaussian and t copula are then used to model the joint distributions of these factor log-returns. The models developed are applied to estimate the one-day ahead Value-at-Risk (VaR) in testing data. The estimations of the VaR are backtested to check for correct unconditional coverage and exponentially distributed durations between exceedances. The results suggest that the ARMA-NGARCH processes are a valid approximation of the factor log-returns, and lead to good estimations of the VaR. The results of the multivariate analysis suggest that constant Gaussian and t copulas might be insufficient to model the dependence structure of the factors, and that there might be a need for more flexible copula models with dynamic correlations between factor log-returns. / Fama och Frenchs trefaktormodell har blivit en populär modell för aktieavkastning, och utvidgades nyligen av Fama och French genom att två ytterligare faktorer lades till för att skapa en femfaktormodell. Carthart föreslår en annan modell där trefaktormodellen kompletteras med en momentumfaktor. Då dessa faktorer används inom både akademiska sammanhang och kapitalförvaltning finns det ett tydligt behov av att undersöka vilka egenskaper fördelningen av faktorernas avkastning har. Dock har tidigare sådan forskning inte undersökt detta för alla sex faktorer, och endast använt data från USA:s marknad. I detta examensarbete undersökt därför sannolikhetsfördelningen för den logaritmiska dagliga avkastningen av de fem Fama-French-faktorerna och Cartharts momentumfaktor i europeisk data från åren 2009 till 2019. De endimensionella sannolikhetsfördelningarna modelleras som dynamiska med hjälp av ARMA-NGARCH-processer med feltermer som är fördelade enligt en generaliserad t-fördelning som tillåter skevhet. För att modellera multivariata fördelningar används en Gaussisk copula och en t-copula. De erhållna modellerna används sedan för att uppskatta daglig Value-at-Risk (VaR) i testdata. Dessa uppskattningar av VaR genomgår sedan statistiska test för att undersöka om antalet överträdelser är korrekt och tiderna mellan varje överträdelse är exponentialfördelade. Resultaten i detta examensarbete tyder på att ARMA-NGARCH-processer är en bra approximation av faktorernas logaritmiska dagliga avkastning, och ger bra uppskattningar av VaR. Resultaten för den multivariata analysen tyder på att en konstant copula kan vara en otillräcklig modell för beroendestrukturen mellan faktorerna, och att det möjligen finns ett behov av att använda mer flexibla copula-modeller med en dynamisk korrelation mellan faktorernas logaritmiska avkastning.

The Kikae dialect is a regional variety of Swahili spoken in the southern part of Unguja, the largest island of the Zanzibar archipelago. In this dialect, the morpheme -wa preceded by a subject prefix, which agrees with the subject in person or noun class, is used as a copula. This form is used in neither Standard Swahili nor the Kiunguja dialect considered prestigious dialects of Swahili. In this paper, I describe the morphological and semantic characteristics of this copula, which have not been observed in previous studies, and propose a possible grammaticalisation path of the copula based on its synchronic properties and typological evidence. The following three claims will be made: 1. the subject prefix -wa morphologically corresponds to the perfect form, but does not encode a prior event unlike the perfect form of other verbs. 2. The use of the subject prefix -wa copula is restricted to ‘predicational sentences’. 3. It is highly probable that the subject prefix -wa has grammaticalized from a locative verb

Credit derivatives are instruments that transfer the credit risk from one party to another one. The most common credit derivative is the single entity credit default swap (CDS).A basket default is similar to a single entity CDS except that the underlying obligation is a basket of entities rather than a single reference asset. The copula methods play an important role while we price a multiname product since the assets in the portfolio are not independent. We need to model the correlated default times by using copula functions. In this article, we develop a copula based methodology for pricing -to-default swaps by using market CDS quotes. In order to know the influence of changing price drivers such as correlations and intensities on spreads, we also discuss the sensitivity analysis in this article.

Collateralized debt obligations (CDOs) represent one of the fastest-growing credit derivatives of the structured finance world. In January 2007, the law has been promoted so that CDOs can be issued in Taiwan, including CLOs and CBOs. Thus, we can expect that these two kinds of CDOs will be main products in short future. There are many approaches to valuing CDOs, such as structural models, reduced-form models and credit barrier models. Copula models, which are sometimes classified as reduced-form models, represent the market standard for pricing CDOs. In this paper, we discuss the “implied copula model”, one approach implied from copulas. This is first written by John Hull and Alan White in October, 2006. Here, we discuss how the assumptions in the implied copula model can be released or changed. In our study, we use the CDX IG data on June 8, 2007, for calibration. Besides valuing CDOs with implied copula, we use the adjusted implied copula approach to hedge. Since credit default swap (CDS) has become one of the basic credit products and CDOs are based from some set of CDSs, the CDO tranches and the CDSs must be arbitrage-free. By taking this idea into our model, our study shows that this approach can be used to hedge CDOs with CDSs. Moreover, we use implied copula to eliminate the arbitrage opportunity in Gaussian copula/base correlation approach. As valuing, we also use the CDX IG data on June 8, 2007, for calibration in our hedging model. Consequently, our results suggest that there is a hedging approach with better hedging effect, which is constructed according to Greeks of CDO tranches or according to classification by industries and credit ratings of the CDS names for CDOs.

We consider the problem of calculating tail probabilities of the returns of linear asset portfolios. As flexible and accurate model for the logarithmic returns we use the $t$-copula dependence structure and marginals following the generalized hyperbolic distribution. Exact calculation of the tail-loss probabilities is not possible and even simulation leads to challenging numerical problems. Applying a new numerical inversion method for the generation of the marginals and importance sampling with carefully selected mean shift we develop an efficient simulation algorithm. Numerical results for a variety of realistic portfolio examples show an impressive performance gain. (author´s abstract) / Series: Research Report Series / Department of Statistics and Mathematics