此研究主要研究壽險業的系統性風險與違約風險之評價，基於投資組合的波動度去建立隨機過程模型。特別是那些隱含無法被多角化的財務風險、系統性風險，透過研究，使用Heston(1993)模型去描述標的資產的隨機波動程度比以往使用Black-Scholes(1973)模型描述股價的波動變化更能反映實際的風險狀況，並透過CIR過程來表示瞬間的波動程度。在這個模型之中，把過去以平賭測度決定違約選擇權的方法延伸。此外透過探討違約價值之敏感度，根據不同的情境測試對於壽險公司負債的影響。最後透過數值的結果與敏感度分析隨機波動模型與確定性的模型之差異。 當資本準備增加時，資產與負債比提高，因負債仍固定承諾予保戶之利率增長，而資產因應系統性風險的發生而減損仍能支付負債，致使違約風險降低，進而使得評價時點的違約金額降低。當系統風險發生時，風險值上升，違約價值為右偏分布，代表在極端條件下有可能有極大的損失；反之，當整個金融體系經濟情勢良好，公司擁有足夠的經濟資本時，風險值下降，滿足VaR75與CTE65的法規限制，此時公司的清償能力足以反映系統性風險。 / This paper considers the problem of valuating the default option of the life insurers that are subject to systematic financial risk in the sense that the volatility of the investment portfolio is modeled through stochastic processes. In particular, this implies that the financial risk cannot be eliminated through diversifying the asset portfolio. In our work, Heston (1993) model is employed in describing the evolution of the volatility of an underlying asset, while the instantaneous variance is a CIR process. Within this model, we study a general set of equivalent martingale measures, and determine the default option by applying these measures. In addition, we investigate the sensitivity of the default values given regulatory forbearance for the life insurance liabilities considered. Numerical examples are included, and the use of the stochastic volatility model is compared with deterministic models. As reserve of capital is increasing, asset-liability ratio is also increasing. The liability grew up with promised interest rate, and it could be covered by the asset when the systematic risk events happened. Therefore, the default risk was decreasing, that caused the default value decreasing. When the systematic risk events happened, the value of risk was increasing, and the default value was positive skew distribution. That means the maximum loss will be coming in the extreme case. On the other hand, when prosperity economy occurred, the value of risk was decreasing, which in compliance with the law of VaR75&CTE65 rules, and the insurance company had enough capital to face the systematic risk events.

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.

本文引用Petkova(2006)所制定出來的模型及概念，探討Fama-French因子是否能作為投資機會的預測變數，並分析台灣股票市場風險溢酬(risk premium)與總體經濟變數間的關係。本文使用的總體經濟變數包括：規模效果因子(SMB)、淨值市價比效果因子(HML)、市場因子(market factor)、違約利差(default spread)、期限利差(term spread)、一個月期定存利率(RF)及股利收益率(dividend yield)。除此之外，本文亦以VAR系統表達每個狀態變數的動態特徵，討論公司治理因子與總體經濟變數(macroeconomic variables)間的關聯，並比較總體經濟變數與公司治理因子分別對股票超額報酬的解釋能力。 本研究以台灣股票市場為研究樣本，資料期間為2005年11月至2014年4月，共102個月的月報酬為研究主體。實證結果可發現：（1)本研究的價值型的股票(value stock)具有較高的風險溢酬，成長型股票(Growth stock)擁有較低的風險溢酬；而台灣上市公司也存在顯著規模效果，小市值公司具有較高的風險溢酬，大市值公司擁有較低的風險溢酬。（2)在大市值的分類下，期限利差(term spread)與淨值市價比因子(HML)呈現正向變動。在小市值的分類下，期限利差(term spread)與淨值市價比因子(HML)呈現反向變動；違約利差(default spread)則與規模效果因子(SMB)呈現正向變動。 / We use the model and concept that Petkova(2006) formulated to discuss if Fama-French factors can be the predictable variables of investment opportunity and analysis the relationship between risk premium and macroeconomic variables on Taiwan stock market. There are many macroeconomic variables in the article：Size factor(SMB)、book-to-market factor(HML)、market factor、default spread、term spread、one-month deposit interest rate and dividend yield. We capture the dynamic characters of every variables through VAR system to analyze the relationship French-French factors and macroeconomic variables. Furthermore, we compare the relationship between SMB and default spread, HML and term spread through the first step of Fama-MacBeth way. We can make two important conclusions through empirical evidence：(1) The risk premium is higher in value stocks than in growth stock, which means there is prominent book-to-market effect on Taiwan stock market. Moreover, the risk premium is higher in small firms than in large firms, which means there is magnificent size effect on Taiwan stock market.（2) The behavior that default spread has is the same as SMB factor in any book-to-market ratio criteria. However, the behavior that term spread has is the same as HML factor only in big capitalization criteria.

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.

本研究分為兩個部份，第一部份提出評價選擇權時，應考慮加價利益(Mark-Up Interest)的觀點，第二部份則提出信用違約交換選擇權的新評價模型。 在第一部份，所謂加價利益是指選擇權賣方為彌補採取避險組合後仍可能發生的損失而向選擇權買方收取的風險補償。本研究的方法是將選擇權市價拆解成理論公平賭局價格與加價利益，建立包含加價利益、買賣權平價理論、隱含標的價格與猜測波動度的選擇權評價模型，解決隱含波動度微笑(implied volatility smile)所帶來模型內部不一致的問題。在建立各種情境條件下之加價利益後，可用來評估選擇權市價的合理性，以提升買賣雙方對市價的合理判斷，有利於風險管理者進行選擇權之造市操作與避險。本研究經由對台指選擇權(TXO)的實證結果發現：加價利益受到距到期交易日、價況程度(moneyness)及猜測波動度的影響。 第二部份所提出之信用違約交換選擇權的新評價模型則是延伸Schonbucher ( 2000, 2003, 2004 )、Brigo ( 2004, 2005a, 2005b, 2006 )、Brigo & Mercurio ( 2006 )、Brigo & Morini ( 2005 )、Jamshidian ( 2004 ) 與Wu ( 2006 ) 的研究，以市場上交易之各年期信用違約交換之商品所導出之費率期間內之各單期( single tenor )遠期信用違約交換率之費率端價值做為計價資產，假設各單期遠期違約交換率為對數常態分配下，可以將信用違約交換選擇權拆解為由各單期加總之違約交換選擇權，應用在投資銀行發行許多相同標的但不同起始日、不同到期日之一系列信用違約交換選擇權( CDS options )時，可以具有評價簡易的優勢，吻合各期間之信用市場狀況，避免套利機會，並能運用信用違約交換( CDS )，增進避險與管理信用風險之技術。 / This thesis is composed of two parts. The first part is the standpoint of the “Mark-Up Interest” on options. The second part is the new model about pricing and hedging on credit default swap options. In the first part, the Mark-Up Interest is regarded as the reward on the hedging portfolio to compensate for possible losses. For presenting this, options market prices are decomposed into the fair-game options prices and the Mark-Up Interests. The options pricing model formed with the Mark-Up Interest, put-call parity, implied underlying price, and guessed volatility is used to solve the internal inconsistence caused by the implied volatility smiles. Therefore, the justness of the options market prices could be estimated with the Mark-Up Interests under different scenarios. The result will help the risk manager to do market making and hedging. The empirical results based on the Options on Taiwan Stock Exchange Weighted Stock Index (TXO) in this paper are as follows: The trading days to expiry, moneyness, and guessed volatility are the factors affecting the Mark-Up Interests. The second part of this thesis extends the research on Schonbucher ( 2000, 2003, 2004 ), Brigo ( 2004, 2005a, 2005b, 2006 ), Brigo & Mercurio ( 2006 )、Brigo & Morini ( 2005 ), Jamshidian ( 2004 ) and Wu ( 2006 ). We use the fee leg of the single tenor forward credit default swap rate ( tenor CDS rate ) as numeraire. Under the lognormal distribution assumption on the tenor CDS rate, we decompose a credit default swap option into the sum of tenor CDS options. The result can be used by investment banks to manage credit risk when their derivative book consists of different start-date and end-date CDS options. In addition, our result shows that CDS can be used to hedge against the risk of CDS options. The proposed method helps improve the techniques of hedging and managing credit risk.

本研究以事件研究法的方式，研究歐洲央行宣布量化寬鬆（Quantitative Easing, QE）對歐豬五國信用風險的影響，本研究以各國主權信用違約交換的超額報酬顯著性衡量量化寬鬆政策對信用風險的影響。 研究結果為多數的QE政策宣告對歐豬五國信用風險的影響在事件期中有正向有負向，且時常交錯分布，未有一固定的模式，故無法得到一個明確的結論。 / This paper examines the impact of the ECB’s (European Central Bank) quantitative easing program on the credit risk of PIIGS. In this case, we used each underlying countries’ excess return of their sovereign CDSs to identify if their credit risks are decreased significantly. Our finding was that most QE announcements by the ECB had multiple impacts on the credit risk of PIIGS. They had both positive and negative impacts. Also, the patterns were not the same, so we do not have a clear conclusion on whether the QE policies are good or bad for the credit risk of PIIGS.

本論文將針對不同證券化標的型態和考量房貸戶提前清償差異之情況下，來推導MBS的評價公式。其中可發現任何證券化標的型態的MBS評價過程都能從可調整利率住宅抵押貸款的角度來進行，因此建構出的一般化評價模型便可作為其他新奇房貸設計的參考依據。並且透過蒙地卡羅法來模擬可調整利率住宅抵押貸款的理論價值，同時採用反向變異法來達到加速模擬過程的目的，以便於更趨近於真正的理論價值。而且也針對建構模型中的各項參數、誘因函數參數以及其他影響MBS理論價值的因素進行敏感度分析。

過去金融市場尚未發達的年代，利率常常被當作貨幣的價格看待，利率變動，投資人只能享受定存利率上升之外，很難有其他的獲利變化。不過這幾年來，好不容易金融市場開放，財政部、櫃檯買賣中心都分別開放金融機構取得「結構型商品」和「利率衍生性商品」的業務執照，許多銀行與券商立刻將兩者結合，推出連動利率之商品，總算替這些期盼已久的投資客開啟另一扇追求利潤的大門。此外，經過近30 年的發展，衍生產品市場正日益成為現代金融業的主流之一。雖然在20 世紀90 年代初期，衍生產品的交易與創新都僅限於市場性風險，然而，金融業面臨的風險之一是信用風險，卻未能在此領域大放光彩。不過，信用風險管理的新工具—信用衍生產品（Credit Derivative），已經慢慢蓬勃發展，因為大量需求而交易熱絡。1996 年，信用衍生產品交易額已達到400 億美元，日前則已超過1000 億美元。儘管目前信用衍生產品的交易量與一般的利率衍生產品交易量尚難並駕齊驅，但由於信用風險管理領域市場還是相當的開闊，相信在進入21 世紀之後，鼎盛時期之來臨並不遠矣，如同其他的衍生產品一樣，它將對未來金融業產生廣泛而深遠的影響。 故本文運用Kijima and Muromachi（2000 ,KK）之模型，評價多標的的信用違約交換；同時利用Hull-and-White 之利率模型，評價逆浮動結構性債券，以解析解評價出合理價格；並以市場上已發行一籃子信用連動式債券與雪球式利率連動式債券為例，計算出合理價格，最後提出避險工具及探討，給予投資人明確的投資訊息，跳出資訊不對稱的空間；促成投資者與發行商雙贏的局面。

近年來，信用衍生性金融商品蓬勃發展，市場上陸續出現不同特色的信用擔保憑證。過去評價信用衍生性金融商品多採用Hull & White (2004)年所發表的因子相關結構型模型(factor copula approach)。由於因子相關模型在描述違約事件，可降低處理維度，使得計算更容易處理，更方便建立出損失分配，讓評價工作更順利進行。但是，降低維度的便利，卻犧牲了違約時點的動態描述，在因子模型中，我們無法掌握損失分配的期間結構，所以只能處理單一到期日的信用衍生性金融商品。 但市場上逐漸出現具有時間相關性的信用金融商品，例如：遠期生效型信用擔保憑證(Forward-starting CDO)、信用擔保憑證分券選擇權(Option on CDO tranches)、重設型信用擔保憑證等。其中遠期生效契約的特色在於，在生效日之前，標的資產若違約，並不構成損失的發生，只會將此商品從投資標的中剔除。故投資人在生效日之前，受到一層信用保護，所以相較於同天到期的信用擔保憑證，會使遠期契約的信用價差會比較低，可降低發行商的成本。在加上近年來，信用曲線出現越來越陡峭的情形，代表到期日相差越長，報酬差異越大，所以投資較長天期的商品，相對報酬提高較多。而次順位分券信用價差近年來下降許多，不少投資人為了達到報酬目標，轉而投資較長天期的信用投資產品。而且信用曲線過於陡峭，投資人預期未來違約環境會呈現平緩或變佳的趨勢，可以透過購買遠期契約，來獲得投資利潤。 由於我們不想放棄因子相關性結構模型在使用上簡便的優勢，所以試圖將跨期相關因子引入因子模型，將期間之間的相關性考慮進去，讓遠期生效信用擔保憑證的評價工作得以運行。除此之外，我們分析各分券對參數的敏感性，並加以探討其中的經濟意涵，最後以討論遠期信用擔保憑證避險的策略作結。