資產證券化源自1970年代，第一筆擔保債權憑證交易自1988年出現在美國，然後在歐美迅速發展，目前已成為重要的之債券市場。台灣金融產業發展正值轉型期，銀行除面對低利率帶來經營壓力之外，同時亦需規避評等較差之企業貸款的信用風險，而保險業者在低利率時代來臨卻無良好報酬之投資標的可供投資。因此，此環境乃為推動證券化之良好契機。自1997年發生東南亞金融危機，乃至1998年韓國的亞洲金融危機，造成許多跨國企業紛紛裁員、關廠、甚至倒閉，造成一連串的金融危機連鎖效應。因此，公司間或產業間之榮枯是相互關聯的，且均會受總體經濟因素所影響。是以，近年來除信用風險亦成為近年來財務領域上重要議題。理論或實證上，當多個標的資產之信用衍生性商品被加以開發，並用來管理信用風險的時候，需考慮多個標的資產間的違約相關性，方能準確地衡量信用風險。故在信用風險管理與信用衍生性商品的評價中，違約相關性的估計與考量顯得格外重要。結構式或縮減式模型在發展違約相關性的多變數模型中是困難的，因為其衍生性商品價值的理論推導繁複或其數值計算是相當費時。本文在多標的資產之信用風險評價模型中，透過適當個別資產之邊際違約機率與Copula函數之選擇，及其相關參數之估算，即可快速求算具違約相關性之多變數聯合機率函數，以利擔保債權憑證(CDO)之評價。因此，本文針對BET、Copula、Factor Copulas等三種方法與分析架構做一剖析，再以國內153家上市公司所發行無擔保債券作為連結標的之擔保債權憑證為例，進行模擬實證並分析結果。

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.

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狀況，使得原始信用風險債券在到期時的本金償付受到其他債券的信用風險影響，因此如何準確且客觀的估計資產池內違約機率便一個很重要的課題，而過去文獻常以給定參數的方式，並且假設資產間的違約狀況彼此獨立下進行評價，對於聯合違約機率的捕捉並不明顯，因此本文延伸Factor Copula模型，建立信用連結債券之評價模型，該模型考慮了資產間的違約相關程度，以期達到符合市場的效果，同時配合統計之因素分析法，試圖找出影響商品價格背後的市場因子。 本研究利用延伸的評價模型以及Copula法，對實際商品做一訂價探討，結果發現，不管是使用樣本內或樣本外的資料去評價時，本研究的評價模型表現都優於Copula法，表示說評價時額外加入市場因子的考慮，對於評價是有正向的幫助；而在因子選取方面，我們選取18項因子後，經由因素分析共可萃取出三大類因素，藉由觀察期望價格與市場報價的均方根誤差，發現國家因素以及產業因素均對於商品價格有所影響，而全球因素對於商品不但沒有顯著影響，同時加入後還會使得計算出的商品期望價格更偏離市場報價，代表說並不是盲目的加入許多因子就能使得模型計算出的價格貼近市場報價，則是要視加入的因子對於資產的影響程度而定。 對於後續研究的建議：由於本研究的實證中存在一些假設，使得評價過程中並不完全符合現實市場現況，若能得到市場上的真實數據，或是改以隨機的方式來計算，相信結果會更貼近市場報價；同時，藉由選取不同的因子來評價，希望能找出國家因素、產業因素以外的其他影響因子，可助於我們更了解此項商品背後的影響因素，使得投資人能藉由觀察市場因子數據來判斷商品未來價格走勢。 / Value of the credit-linked notes depend on the pool of assets whether default or not, so the promised payoff of credit-linked notes is affected by other risky underlying assets. Therefore, how to estimate the probability of default asset pool accurately and objectively will be a very important issue. In the past literature, researchers usually use given parameters, and assume assets probability of default are independent from each other under valuation. Furthermore, it is not obvious to capture the joint probability of default. Thus, this article extends the Factor Copula Model to provide a new methodology of pricing credit-linked notes, which consider the default correlation between the extent of assets in order to achieve result in line with market and with Factor Analysis method added, trying to figure out the impact of commodity price factor behind the market. In the empirical analysis, pricing the actual commodity issued by LB Baden-Wuerttemberg using extend model and Copula model, we found that no matter choose in-the-sample or out-the-sample data to valuation, the models in this article are superior to Copula model by compare the root-mean-square deviation(RMSE). It means add the market factors into our valuation is beneficial. In terms of selection factors, we select eighteen factors prepared by Morgan Stanley Capital International, and three categories of factors may be extracted from Factor Analysis method. By observing RMSE, both national factors and industry factors will influence on the commodity, but world factors not only did not significantly impact on the commodity, but also add it to calculate the expected price further from the market price. Representative said not blind join the many factors can make the model to calculate the price close to the market price, it is a factor depending on the degree of influence of the added asset. For the suggestion of future research. The fact that the presence of empirical assumptions in this study, result in the evaluation process is not entirely realistic to market situation. We suggest to get the real data on the market or use random way to calculate, we believe that the outcome will be closer to the market price. Meanwhile, by selecting different factors to evaluate, trying to discover further factors which significantly impact on the commodity; it will help us better to understand the factors behind the commodity, so investors can predict commodity future prices by observing the market data.

自從1997年東南亞金融風暴，許多跨國企業紛紛倒閉，造成一連串的金融危機連鎖效應，無論是金融機構或投資人皆蒙受巨大的損失，使得金融市場開始正視信用風險的問題，增加對風險管理的重視。除了信用風險的問題外，由於過去幾年利率是一路下滑，使反浮動利率的公司結構債廣受歡迎，如今利率反轉上升，結構債的價格就會下跌虧損，手上握有大筆結構債的基金或是投信公司便因此受到牽連，自2005年起開始發行的CBO，便是為了解決公司結構債的問題而發行。在此環境下，更加速了信用衍生性商品的發展。 資產證券化對金融機構來說，除了有可以將信用風險移轉給投資人的好處之外，也是減低籌資成本的一個管道。另外，還有能增加收入、克服資本限制以及流動性限制等優點。 但在CDO之債權群組中，當債務人間的違約情況具有相關性時，個別債務人發生違約將可能連帶使得整個CDO債務現金流量來源產生嚴重衝擊。因此，如何準確推估CDO與CDO-squared各個分券下合理之信用價差，乃本研究分析商品的重點。 本研究採用Gaussian Copula，並利用蒙地卡羅法以及Probability Bucketing Approach評價擔保債權憑證。雖然Probability Bucketing Approach與蒙地卡羅法所模擬出來的結果很接近，然而Probability Bucketing Approach卻是較有效率的評價方法。在Probability Bucketing Approach中，損失級距的切割將會影響到評價的準確性，切割地越細密，越能準確地計算出損失分配，進而得到精確的信用價差。本文亦發現違約回收率、相關係數、違約率以及債權重複性(Overlap)均會顯著影響分券信用價差的評價，顯示參數正確評估之重要性。

A credit derivative is a financial instrument whose value depends on the credit risk of an underlying asset or assets. Credit risk is the possibility that the obligor fails to honor any payment obligation. This thesis proposes four new computational methods for the valuation of credit derivatives. Compared with synthetic collateralized debt obligations (CDOs) or basket default swaps (BDS), the value of which depends on the defaults of a prescribed underlying portfolio, a forward-starting CDO or BDS has a random underlying portfolio, as some ``names'' may default before the CDO or BDS starts. We develop an approach to convert a forward product to an equivalent standard one. Therefore, we avoid having to consider the default combinations in the period between the start of the forward contract and the start of the associated CDO or BDS. In addition, we propose a hybrid method combining Monte Carlo simulation with an analytical method to obtain an effective method for pricing forward-starting BDS. Current factor copula models are static and fail to calibrate consistently against market quotes. To overcome this deficiency, we develop a novel chaining technique to build a multi-period factor copula model from several one-period factor copula models. This allows the default correlations to be time-dependent, thereby allowing the model to fit market quotes consistently. Previously developed multi-period factor copula models require multi-dimensional integration, usually computed by Monte Carlo simulation, which makes the calibration extremely time consuming. Our chaining method, on the other hand, possesses the Markov property. This allows us to compute the portfolio loss distribution of a completely homogeneous pool analytically. The multi-period factor copula is a discrete-time dynamic model. As a first step towards developing a continuous-time dynamic model, we model the default of an underlying by the first hitting time of a Wiener process, which starts from a random initial state. We find an explicit relation between the default distribution and the initial state distribution of the Wiener process. Furthermore, conditions on the existence of such a relation are discussed. This approach allows us to match market quotes consistently.

A credit derivative is a financial instrument whose value depends on the credit risk of an underlying asset or assets. Credit risk is the possibility that the obligor fails to honor any payment obligation. This thesis proposes four new computational methods for the valuation of credit derivatives. Compared with synthetic collateralized debt obligations (CDOs) or basket default swaps (BDS), the value of which depends on the defaults of a prescribed underlying portfolio, a forward-starting CDO or BDS has a random underlying portfolio, as some ``names'' may default before the CDO or BDS starts. We develop an approach to convert a forward product to an equivalent standard one. Therefore, we avoid having to consider the default combinations in the period between the start of the forward contract and the start of the associated CDO or BDS. In addition, we propose a hybrid method combining Monte Carlo simulation with an analytical method to obtain an effective method for pricing forward-starting BDS. Current factor copula models are static and fail to calibrate consistently against market quotes. To overcome this deficiency, we develop a novel chaining technique to build a multi-period factor copula model from several one-period factor copula models. This allows the default correlations to be time-dependent, thereby allowing the model to fit market quotes consistently. Previously developed multi-period factor copula models require multi-dimensional integration, usually computed by Monte Carlo simulation, which makes the calibration extremely time consuming. Our chaining method, on the other hand, possesses the Markov property. This allows us to compute the portfolio loss distribution of a completely homogeneous pool analytically. The multi-period factor copula is a discrete-time dynamic model. As a first step towards developing a continuous-time dynamic model, we model the default of an underlying by the first hitting time of a Wiener process, which starts from a random initial state. We find an explicit relation between the default distribution and the initial state distribution of the Wiener process. Furthermore, conditions on the existence of such a relation are discussed. This approach allows us to match market quotes consistently.

<p>The dissertation consists of four chapters that concern topics on copulas for high dimensions. Chapter 1 proposes a new general model for high dimension joint distributions of asset returns that utilizes high frequency data and copulas. The dependence between returns is decomposed into linear and nonlinear components, which enables the use of high frequency data to accurately measure and forecast linear dependence, and the use of a new class of copulas designed to capture nonlinear dependence among the resulting linearly uncorrelated residuals. Estimation of the new class of copulas is conducted using a composite likelihood, making the model feasible even for hundreds of variables. A realistic simulation study verifies that multistage estimation with composite likelihood results in small loss in efficiency and large gain in computation speed. </p><p>Chapter 2, which is co-authored with Professor Andrew Patton, presents new models for the dependence structure, or copula, of economic variables based on a factor structure. The proposed models are particularly attractive for high dimensional applications, involving fifty or more variables. This class of models generally lacks a closed-form density, but analytical results for the implied tail dependence can be obtained using extreme value theory, and estimation via a simulation-based method using rank statistics is simple and fast. We study the finite-sample properties of the estimation method for applications involving up to 100 variables, and apply the model to daily returns on all 100 constituents of the S\&P 100 index. We find significant evidence of tail dependence, heterogeneous dependence, and asymmetric dependence, with dependence being stronger in crashes than in booms. </p><p>Chapter 3, which is co-authored with Professor Andrew Patton, considers the estimation of the parameters of a copula via a simulated method of moments type approach. This approach is attractive when the likelihood of the copula model is not known in closed form, or when the researcher has a set of dependence measures or other functionals of the copula that are of particular interest. The proposed approach naturally also nests method of moments and generalized method of moments estimators. Drawing on results for simulation based estimation and on recent work in empirical copula process theory, we show the consistency and asymptotic normality of the proposed estimator, and obtain a simple test of over-identifying restrictions as a goodness-of-fit test. The results apply to both $iid$ and time series data. We analyze the finite-sample behavior of these estimators in an extensive simulation study.</p><p>Chapter 4, which is co-authored with Professor Andrew Patton, proposes a new class of copula-based dynamic models for high dimension conditional distributions, facilitating the estimation of a wide variety of measures of systemic risk. Our proposed models draw on successful ideas from the literature on modelling high dimension covariance matrices and on recent work on models for general time-varying distributions. Our use of copula-based models enable the estimation of the joint model in stages, greatly reducing the computational burden. We use the proposed new models to study a collection of daily credit default swap (CDS) spreads on 100 U.S. firms over the period 2006 to 2012. We find that while the probability of distress for individual firms has greatly reduced since the financial crisis of 2008-09, the joint probability of distress (a measure of systemic risk) is substantially higher now than in the pre-crisis period.</p> / Dissertation

In the last decade, a considerable growth has been added to the volume of the credit risk derivatives market. This growth has been followed by the current financial market turbulence. These two periods have outlined how significant and important are the credit derivatives market and its products. Modelling-wise, this growth has parallelised by more complicated and assembled credit derivatives products such as mth to default Credit Default Swaps (CDS), m out of n (CDS) and collateralised debt obligation (CDO). In this thesis, the Lévy process has been proposed to generalise and overcome the Credit Risk derivatives standard pricing model's limitations, i.e. Gaussian Factor Copula Model. One of the most important drawbacks is that it has a lack of tail dependence or, in other words, it needs more skewed correlation. However, by the Lévy Factor Copula Model, the microscopic approach of exploring this factor copula models has been developed and standardised to incorporate an endless number of distribution alternatives those admits the Lévy process. Since the Lévy process could include a variety of processes structural assumptions from pure jumps to continuous stochastic, then those distributions who admit this process could represent asymmetry and fat tails as they could characterise symmetry and normal tails. As a consequence they could capture both high and low events¿ probabilities. Subsequently, other techniques those could enhance the skewness of its correlation and be incorporated within the Lévy Factor Copula Model has been proposed, i.e. the 'Stochastic Correlated Lévy Factor Copula Model' and 'Lévy Random Factor Loading Copula Model'. Then the Lévy process has been applied through a number of proposed Pricing Basket CDS&CDO by Lévy Factor Copula and its skewed versions and evaluated by V-FFT limiting and mixture cases of the Lévy Skew Alpha-Stable distribution and Generalized Hyperbolic distribution. Numerically, the characteristic functions of the mth to default CDS's and (n/m) th to default CDS's number of defaults, the CDO's cumulative loss, and loss given default are evaluated by semi-explicit techniques, i.e. via the DFT's Fast form (FFT) and the proposed Very Fast form (VFFT). This technique through its fast and very fast forms reduce the computational complexity from O(N2) to, respectively, O(N log2 N ) and O(N ).

1990年代中期信用衍生信商品開始發展，隨著時代變遷，演化出信用違約交換(Credit Default Swaps, CDS)、擔保債權憑證(Collateralized Debt Obligation, CDO)、合成型擔保債權憑證(Synthetic CDO)等商品，其可以分散風險的特性廣受歡迎，並且成為完備金融市場中重要的一環。在2007年金融海嘯中，信用衍生性商品扮演相當關鍵的角色，所以如何合理定價各類信用衍生性商品就變成相當重要的議題 以往在定價合成型擔保債權憑證時，多採取單因子結構模型來做為報酬函數的主要架構，並假設模型分配為常態分配、t分配、NIG分配等，但單因子結構模型的隱含相關係數具有波動性微笑現象，所以容易造成定價偏誤。 為了解決此問題，本文將引用常態分配假設與NIG分配假設下的隨機風險因子負荷模型(Random Factor Loading Model)，觀察隨機風險因子負荷模型是否對於定價偏誤較其他模型有所改善，並且比較各模型在最佳化參數與定價時的效率，藉此歸納出較佳的合成型擔保債權憑證定價模型。 / During the mid-1990s, credit-derivatives began to be popular and evolved into credit default swaps (CDS), collateralized debt obligation (CDO), and synthetic collateralized debt obligation (Synthetic CDO). Because of the feature of risk sharing, credit-derivatives became an important part of financial market and played the key role in the financial crisis of 2007. So how to price credit-derivatives is a very important issue. When pricing Synthetic CDO, most people use the one-factor coupla model as the structure of reward function, and suppose the distribution of model is Normal distribution, t- distribution or Normal Inverse Gaussian distribution(NIG). But the volatility smile of implied volatility always causes the pricing inaccurate. For solving the problem, I use the random factor loading model under Normal distribution and NIG distribution in this study to test whether the random factor loading model is better than one-factor coupla model in pricing, and compare the efficience of optimization parameters. In conclusion, I will induct the best model of Synthetic CDO pricing.

近年全球市場出現一些以信用違約交換(CDS)為基礎來編列之信用指數(credit indices)，如DJ iTraxx Europe與DJ CDX.NA等，而以這些信用指數為參考資產組合之合成型擔保債權憑證(Synthetic CDO)契約也定期被推出，由於其為標準化契約，故次級市場相當具有流動性，使得全球合成型擔保債權憑證無論在交易量或發行量皆成長快速。 　　本研究在單因子相關性結構模型之架構下，利用Hull & White (2004)所提出之機率杓斗法則(Probability Bucketing Method)建立合成型擔保債權憑證之評價模型，並於評價之外增加分券(Tranche)風險衡量指標之計算，我們發現額外得到分券之風險衡量指標僅需增加約4%的程式運算時間。本研究之評價模型同時可用於分券避險參數之求算，且不會有蒙地卡羅模擬法(Monte Carlo Simulation)之下避險參數不穩定的情形。 我們發現分券已實現之損失會使分券所面對之風險下降，而分券的信用增強(Credit Enhancement)遭受損耗則使分券所面對之風險上升，故權益分券(Equity Tranche)於契約前期所面對之信用風險大於契約後期，次償分券(Mezzanine Tranche)則是於契約後期面對較大之信用風險。關於分券避險，我們可選擇利用標的信用指數或單一資產信用違約(Single-name CDS)交換來進行避險。最後我們對分券進行違約相關性(Correlation)與違約回復率(Recovery Rate)之敏感度分析，發現權益分券的信用價差與資產違約相關性呈反向關係，而與違約回復率呈正向關係；相反的，先償分券(Senior Tranche)的信用價差則與相關係數呈正向關係，與違約回復率呈反向關係；兩參數對次償分券信用價差之影響則沒有一定的趨勢。