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.

信用衍生性商品於近十年來已快速發展，為反映信用風險管理的迫切需求，本篇論文將以實證的方式探討信用衍生性市場。尤其著重在信用違約交換市場，因其佔信用衍生性市場的交易量高達45％。本篇論文分別討論以下二個議題：第一個議題乃在探討股票報酬率的峰態係數與信用違約交換報酬率的關係。第二個議題乃著重探討拉丁美洲國家的信用違約交換對阿根廷事件的反應。 / The development of credit derivatives in the past decade has brought about pronounced innovations in the markets. To reflect dramatic demand in managing credit risk, this thesis dedicates to the empirical world of credit derivatives markets. We especially focus on Credit Default Swaps (CDS) market due to its most widely trading in credit derivatives markets, capturing almost 45% of the market shares. This thesis encompasses two essays related to CDS. In the first essay, we attempt to extend empirical explanation of CDS premiums by considering the excess kurtosis of equity return distribution. As well, we show how copula functions can be applied to specify both the dependence structure and the tail relationship between CDS return and kurtosis of equity distribution. We contribute to the better specification of the dependence structure between the CDS return and the corresponding kurtosis, and provide an illustration of its implication which may be misled using conventional methods. In the second essay, we turn to focus on CDS in emerging markets. Thereby, further policy-oriented applications for governments can be extra induced. We empirically study the correlated default at sovereign level in Latin America region due to the eruption of Argentina debt crisis in 2001. A comprehensive understanding of correlated default at sovereign level is of critical importance in several respects. From the government and IMF point of views, the comovement in sovereign credit default swaps can serve as one of the leading indicators of financial crises. From the perspectives of mutual funds and banks, correlated movement which exists in sovereign CDS spreads is regarded as one of the measures of country risk premium. The findings and the associated methodology can provide useful insights not only to policymakers but also to whoever is interested in credit derivatives markets, particularly in emerging markets. From the methodology point of view, applying a copula method to identify the contagion corresponds to the arguments from Bae et. al. (2003) and Dungey and Tambakis (2003), the further challenge is to develop a model for capturing the nonlinear property.

一籃子信用違約交換評價上並不存在公式解，一般是用蒙地卡羅模擬來推估商品價格，然而，因為蒙地卡羅執行速度較慢，往往會需要能夠大規模運行的計算資源以及高成本的硬體，為了減少成本和提高蒙地卡羅的效率就必須從其演算法改進，於是本文利用Chiang et al.(2007)所提出的一籃子信用違約交換演算法來提升一籃子信用違約交換的評價效率，但是該方法採用多元常態分佈假設下的Factor gaussian copula模型進行評價，並不符合市場實際金融市場資料具有不對稱的偏態現象，尤其對未來的環境危機發生的頻率不斷增加，極端事件可能出現的機會也越來越高，基於此問題，本文將Factor t copula、Factor clayton copula、Factor NIG copula以及Modify factor NIG copula與重要性抽樣演算法結合來提昇商品評價的準確度，並且分析各模型與該演算法結合的效果。

信用衍生性商品（credit derivatives）是用於移轉信用風險之契約，契約是由保護買方（protection buyer）與保護賣方（protection seller）所簽定，由保護買方支付保險金（可為躉繳或分期支付）以獲得信用的保護，而保護賣方則需在律定之信用事件發生時支付償金予保護買方做為補償。近年來頻傳金融事件，巴塞爾銀行監理委員會（Basel Committee on Banking Supervision）也不得不制定新版的巴塞爾協定以要求銀行強化信用風險控制與分散，而信用衍生性商品亦有助於信用風險的移轉與抵減的功能。 本篇針對利用conditional Markov chain來建構信用違約交換與第n次信用違約交換之評價模型，並利用模擬的方式來求算出各商品之利差。藉由現實中的資料取得參數的估計值放入模型內則可以模擬出各種不同的狀況，進而做出避險的策略。 此外，本篇亦探討如何利用Gibbs sampler來改良conditional Markov chain的模擬方法，以模擬當信用衍生性商品中的資產組合有傳染效果的情況。

本研究探討評價一籃子信用商品有效率的估計方法，所謂有效率是指計算簡單、快速且能達到變異數縮減，Chiang, Yueh, and Hsieh (2007)提出一個有效演算法，模型中將系統性風險因子與非系統性風險因子視為常態分配，但考慮現實情況系統性風險因子未必為對稱分配，因此本文系統性風險採用偏斜常態分配，而非系統性風險為常態分配。根據Chiang, Yueh, and Hsieh (2007)所提之演算法，並將其延伸至多個系統性風險因子，探討此方法在系統風險為偏斜常態分配下變異數縮減的效果。以不同的投資組合計算其違約給付金額，並與蒙地卡羅法模擬結果比較，由於此方法皆在至少有k個違約發生的事件下抽樣，因此所需模擬次數較少，計算時間也較短，且可達到變異數縮減。 單一系統性風險因子模型，當 ρ 值高，變異數縮減效果越好，且變異數縮減的效果也隨著 k 值越大效果越好。在二個系統性風險因子模型，變異數縮減的效果也是隨著 k 值越大效果越好。就各因子的權重而言，變異數縮減的效果原則上對權重較大的因子做重點抽樣，變異數縮減效果較顯著，但是此方法對於極為右偏的分配時，對權重較大的因子做重點抽樣效果不彰，此時反而針對對稱分配做重點抽樣的效果較佳。此方法就到期時間做探討，發現到期時間越長變異數縮減效果越差。

歐式信用違約交換選擇權通常都以短天期較富流動信，造成這樣情形的原因很可能是因為長天期的信用違約交換選擇權必須承擔標的公司的倒閉風險。美式信用違約交換選擇權讓持有者可以在選擇權到期以前履約，這使得持有者可以只注意信用違約交換溢酬的變動，而不必擔心標的公司的倒閉風險。在這篇論文當中，我們結合最小平方法以及單期信用違約溢酬模型評價美式信用違約交換選擇權，其中單期信用違約溢酬模型是由布瑞格在2004年所發表的模型。本篇論文評價方法的最大優點在於此方法類似於利率理論的市場模型，因此我們可以利用類似的想法評價任何與信用違約交換合約相關的信用衍生性商品。 / The most liquid European CDS options are usually of short maturities. This may result from that options with longer maturity have to bear more default risk of the reference company. American CDS options allow the holders to exercise options before option matures so that they can focus on spread movements without worrying about default risk. In this paper, we price American CDS options with one-period CDS spread model presented by Brigo (2004). The primary advantage of this model is that it is similar to LIBOR market model in interest rate theory. Therefore, path-dependent CDS-related products can be easily priced with familiar ideas.

相較於單一信用違約交換只能對單一信用標的進行信用保護，一籃子信用違約交換則能對一籃子的信用標的進行信用保護。此種產品的評價決定於一籃子信用標的實體的聯合機率分配，因此多個標的資產間違約相關性的衡量，對於一籃子信用違約交換的評價和風險管理是相當重要的課題。 　　在一個資產池中，有時可以將其切割成兩個以上的群體，各群體間彼此相互獨立，而在各群內彼此相依。我們將其視為在多因子模型下的特例，此模型提供我們更具彈性的方式去建立資產之間彼此的相關性。 　　在這篇文章中，我們主要以 Chiang, Yueh, and Hsieh (2007) 在單因子模型下所提出來的方法為基礎，將其延伸至多因子的模型下的特例。藉由選擇一個合適的(IS)分配，在每一次的模擬中必定會有k個違約事件發生；因此我們獲得一個有效率的方法對一籃子違約交換進行評價，此演算法不僅簡單並且其變異數較蒙地卡羅小。 / In contrast to a single name credit default swaps which provides credit protection for a single underlying, a basket credit default swap extends the credit protection to portfolio of obligors with the restriction that the default of only one underlying is compensated. The price of the products depends on the joint default probability of the underlying in the credit portfolio. Thus, the modeling of default correlation, default risk and expected loss is a key issue for the valuation and risk management of basket default swaps. Sometimes a pool of underlying obligors can have two or more separate groups, between those they are unrelated, but in each part they are related. The special cases provide more flexible way to construct the correlation between two or more underlying obligors. In this paper, our approach is based on the construction of importance sampling (IS) method proposed by Chiang, Yueh and Hsieh (2007) under one-factor model, and then we extend the model to a special case under the multi-factor model. By the appropriate choice of the importance sampling distribution, we establish a way of ensuring that for every path generated, k default events always take place. Then we can obtain an efficiency algorithm for basket default swap valuation. The algorithm is simple to implement and it also guarantees variance reduction.

The first-to-default Credit Default Swap (CDS) with multiple assets is priced when the default barrier is changing over time, which is contrast to the assumption in most of the structural-form models. The survival function of each asset follows the lognormal distribution and the interest rate is constant over time in this article. We define the joint survival function of these assets by employing the normal and Student-t copula functions to characterize the dependence among different default probability of each asset. In addition, we investigate the empirical evidences in the pricing of CDS with two or three companies by changing the values of parameters in the model. The more interesting results show that the joint default probability increases as these assets are more positive correlated. Consequently, the price of the first-to-default CDS is much higher.

近年來由於金融自由化的發展，台灣已陸續開放新金融商品，除了股權相關的新金融商品之外，也陸續開放利率相關的新金融商品，如新台幣利率交換、新台幣利率選擇權、債券遠期交易、債券選擇權等。在信用衍生性商品市場方面，我國銀行從2002年底開放承做信用衍生性商品，目前正準備開放證券商承做。隨著金融國際化及自由化，未來將會從國外引進更新穎的金融商品，使金融市場更為完備。 本文以Hull – White的信用違約交換評價模型及BGM市場利率模型為架構，藉由數值方法評價分析兩個衍生性商品──信用連動票券及美元利率區間保本票券。首先在信用連動票券方面，評價方式主要分為兩個階段。第一，需先計算違約機率，違約機率的求算，即利用風險性債券與無風險性債券價格的差異，衡量可能違約的成本，藉由違約成本推算出發生違約的機率。第二，利用信用保護買方期望未來支付和信用保護賣方期望未來賠償的現值相等關係，來計算信用違約交換利差。 其次在美元利率區間保本票券方面，利用BGM市場利率模型並以蒙地卡羅模擬法（Monte Carlo），來評價此連動債券的理論價格，再進行發行者損益兩平分析和避險分析。最後針對兩個商品的評價結果作結論，分析發行者及投資人的利潤及風險關係，並給予後續研究者模型改進之建議與方向。

固定期信用違約交換(Constant Maturity Credit Default Swap)是移轉固定年期信用違約交換信用價差(CDS Spread)變動風險的信用衍生性金融商品，目前僅Brigo(2005)以及Krekel and Wenzel(2006)探討固定期信用違約交換的評價，也各自推導出近似封閉解，但對於相關參數之估計以及避險參數並沒有涉及，因此本研究將利用歷史資料估計Krekel and Wenzel(2006)評價公式中的參數，讓評價模型更加完備，並求算避險參數，提供發行商與投資人避險資訊。 本文利用目前信用違約交換(Credit Default Swap)市場中各到期日流動性較高的美國Eastman Kodak Company公司債作為標的物，發行一檔固定期信用違約交換，並利用現有市場資訊估計模型中的參數。在避險實證上，本文利用標的物債券信用價差曲線的變動，對固定期信用違約交換契約價值以及五年期及十年期信用違約交換契約價值的影響，建構了一個避險投資組合，使得避險後總投資組合價值波動減少。 / Constant Maturity Credit Default Swap (CMCDS) is one of the credit derivatives, whose function is to circumvent the fluctuating risk of CDS Spread. Brigo (2005) and Krekel and Wenzel (2006) focused on not only probing into the evaluation of the CMCDS but also deriving the approximated closed-form solution in their recent research separately. However, they seldom concern the hedging approach and the estimated parameters of pricing model, which could be major variable in the measurement. This paper is aiming to calculate the history data of hazard rate to estimate the parameters by using the formula from Krekel and Wenzel (2006) and compute the hedging approach of the pricing model to make it become more complete and provide the hedging information for both financial institutions and investors. By using the corporation bond of Eastman Kodak Company which with higher liquidity and various maturity as the main reference asset to issue a CMCDS and utilizing the current available market data to estimate the parameters of the pricing model to evaluate the value of the product, I find that the various credit spread curve of reference bond will influence the value of CDS and CMCDS and try to structure a hedging portfolio to eliminate the fluctuation of the product.