這次的金融海嘯重擊結構型商品市場，結構型商品市場目前正處於過度時期，商品設計勢必朝向簡單化及透明化，故本文選擇市場上常見的利率及股權商品，期望從投資人角度出發，讓投資人對於商品有更進一步的了解。在利率商品中，本文挑選累計區間贖回連動債，該債券連結標的為十年期交換利率，其計息方式為觀察每天交換利率是否落入區間，故本文採用在即期測度下之BGM模型來模擬每天之遠期利率。波動度結構之估計是採用參數化波動度函數來模擬市場上波動度之駝峰現象；相關係數矩陣之校準則是採用遞迴投影。在股權商品中，本文選擇元大證券所發行之一年期機不可失商品，該商品為連結台灣電子產業中之四檔股票，其報酬型態對投資人來說看似優渥，然而在模擬過程中發現其實不然，讓本文了解到如果不對商品有深入之探討，往往也遭受到表面之矇騙。

近幾年來，衍生性商品蓬勃發展，因應投資交易者的投資需求，發行商發行為數眾多的創新商品。市場上投資交易者分為三種類型：避險者、投機客及套利者。避險者使用衍生性商品降低暴險部位，避免因標的波動而使資產減損；投機者則具備對標的走勢的看法，欲操作衍生性商品獲利；最後，套利者會試圖在可容忍的低度風險下，找尋市場上定價不合理的商品，經由買賣套利的操作而獲利。市場上的商品五花八門，各種類型的交易者皆會盡力尋找評價及避險的方法。 　　但是，2007 年美國的次級房貸引起全球金融海嘯的肆虐，投資人對衍生性金融商品產生恐懼，在輿論下，各方忽略衍生性金融商品扮演著促進市場效率性及完整性的角色、風險控管的工具、以及豐富投資人的投資選擇等優點。然衍生性金融商品的發展及其市場的建構仍重要，不應扼殺之。 　　本文期能提供市場一個能應用於實務情況的評價方法，採用 Brace, Gatarek, and Musiela(1997) 的 LIBOR 市場模型及 Longstaff and Schwartz(2001) 的最小平方蒙地卡羅法，評價每日計息雙區間可贖回債券，此屬利率連動債券之一。另外，亦對屬股權連動債券的觸及失效絕對報酬股權連動債進行評價。希望藉由結構型商品評價及敏感度分析，讓發行機構及投資人都能對於商品的報酬及風險有更進一步的瞭解及參考。

利率模型從早期的短期利率模型、遠期利率模型發展到現在的市場模型。在模型的概念上，已經從市場上不存在的瞬間連續利率修正到市場上可觀察的區間連續的遠期利率。而評價方法的進步，使得市場上發展出各式各樣的利率衍生性商品，其中付「提前贖回條款」的債券很常見。為吸引投資人，附提前贖回條款的債券往往伴隨著高配息。本文選用「12年期美金計價『利率區間』連動債券」與「十年期美元計價息滿到期反浮動利率連動債券」做個案分析，在市場模型之下，評價具提前贖回條款的債券。

In this thesis, the interest rates derivatives and their valuation based on the future development of interest rates are presented. The Hull-White model focusing on the modeling of the instantaneous spot rates is described in detail. The model is calibrated to the market caplet volatilities and is used to evaluate various interest rates derivatives. The main emphasis is put on the LIBOR market model describing the development of set of forward rates. There are presented and in detail discussed results of the calibration of LMM model on the market swaption volatilities. At the end the two models are compared.

本文主要評價與分析兩種結構型債券：一為目標贖回雪球型利率連動債、一為雙匯率連動債。 第一個商品利率連動債券為十年期、每季付息債券，其指標利率為三個月期LIBOR利率。本文以BGM市場模型進行評價，同時考慮40個遠期三個月期LIBOR利率的動態過程，而每個動態過程之間的相關係數為一40維度的方陣，為了加速計算速度採用Weigel(2004)運用線性代數降秩的方法，使原本相關係數矩陣由「秩40」降為「秩11」後，不僅可以加快運算速度又不會使原本相關係數矩陣失真。以蒙地卡羅模擬利率路徑評價後並進行敏感性分析。 第二個商品雙匯率連動債券連結到兩個匯率指標：歐元兌日圓及美元兌新台幣。其中連結歐元兌日圓匯率的報酬型態為雙界限出局二元選擇權，而連結美元兌新台幣匯率的報酬型態為下出界選擇權。本文利用Ritchken(1995)三元樹分別建構兩個匯率界限選擇權的評價，並發現歐元兌日圓匯率界限選擇權的價值佔債券面額的比例極小，故之後只針對美元兌新台幣匯率界限選擇權進行敏感性分析。

本文採用BGM模型評價兩個配息型態不同的利率連結商品。利用BGM模型，我們可以直接透過蒐集市場資料，即可描述LIBOR利率的期間結構。同時，對模型內遠期利率波動度與相關係數進行校準(Calibration)，使評價更為正確。 而本文評價的第一個商品為「三年期美元每日計息雙指標利率連動債」，第二個商品則是「10年期歐元逆浮動連動債」。使用BGM模型，並透過最小平方蒙地卡羅模擬，考慮提前買回條款及計算各期的配息，分別求得兩個商品的合理價格並計算避險參數。此外，從發行商與投資人的角度，分別給予避險與投資建議。 關鍵字：利率連動債、每日計息、逆浮動、BGM模型、LIBOR Market Model、Least-Squares Monte Carlo

隨著財務工程學的發展，結構型商品的架構日趨複雜，連結標的也更加多元化，可依投資人對市場未來的預期，設計出不同的商品型態，滿足投資人財富管理的需求或企業理財的規劃。但因為一般投資人不容易了解結構型商品複雜的設計，可能發生投資報酬不符預期或忽略商品潛在風險的情況。 本論文以建華銀行「美金組合式商品連動債券」與「固定期限交換利率利差連動債券」為例，進行評價與避險分析，以互換選擇權推導極小值選擇權的評價方法推導次小值選擇權的封閉解，並與蒙地卡羅模擬結果相較；利用對數常態遠期LIBOR利率模型評價連結固定期限交換利率的商品。最後進行投資與避險策略分析。希望能增進投資人對商品風險與報酬的認識，和提供金融機構未來設計相關類型商品時，對於評價與避險之理論基礎和方法的一個參考。

本論文第一章將 LIBOR 市場模型加入股價動態，並求出其風險中立過程下的動態模型，並利用此模型評價股籌交換契約。第二章將 LIBOR 市場模型擴展成兩國的市場模型，加入兩國股價動態，並求出風險中立過程下的動態模型，並利用此模型評價跨國股籌交換契約。本論文第二部份說明如何實際使用此模型，並使用蒙地卡羅模擬檢驗此評價模型的正確性。 / This thesis includes two main chapters. Chapter 2 is entiled as "Equity Swaps in a LIBOR Market Model" and Chapter 3 is entitled as "Cross-Currency Equity Swaps in a LIBOR Market in a Model". The conclusions of this thesis are made in Chapter 4. In Chapter 2, we extends the BGM (Brace, Gatarek and Musiela (1997))interest rate model (the LIBOR market model) by incorporating the stock price dynamics under the martingale measure. As compared with traditional interest rate models, the extended BGM model is easy to calibrate the model parameters and appropriate for pricing equity swaps. The general framework for pricing equity swaps is proposed and applied to the pricing of floating-for-equity swaps with either constant or variable notional principals. The calibration procedure and the practical implementation are also discussed. In Chapter 3, under the arbitrage-free framework of HJM, we simultaneously extends the BGM model (the LIBOR market model) from a single-currency economy to a cross-currency case and incorporates the stock price dynamics under the martingale measure. The resulting model is very general for pricing almost every kind of (cross-currency) equity swaps traded in OTC markets. The calibration procedure and the hedging strategies are also provided in this paper for practical operation. The pricing formulas of the equity swaps with either a constant or a variable notional principal and with hedged or un-hedged exchange rate risk are derived and discussed as examples.

This thesis is focused on the study of advanced methods of interest rate mo- dels calibration. The theoretical part provides introduction to basic terminology of financial mathematics, financial, concretely interest rate derivatives. It presents interest rate models, it is mainly aimed at HJM approach and describes in detail the Libor market model, then introduces the use of Bayesian principle in calcula- ting the probability of MCMC methods. At the end of this section the methods of calibration of volatility to market data are described. The last chapter consists of the practical application of different methods of calibration Libor market model and consequently pricing od interest rate swaption. The introduction describes procedure of arrangement of input data and process of pricing of interest rate derivatives. It is consequently used for the valuation of derivative contract accor- ding to mentioned methods. 1

In this thesis, the pricing of counterparty credit risk on an OTC plain vanilla interest rate swap is investigated. Counterparty credit risk can be defined as the risk that a counterparty in a financial contract might not be able or willing to fulfil their obligations. This risk has to be taken into account in the valuation of an OTC derivative. The market price of the counterparty credit risk is known as the Credit Value Adjustment (CVA). In a bilateral contract, such as a swap, the party’s own creditworthiness also has to be taken into account, leading to another adjustment known as the Debit Value Adjustment (DVA). Since 2013, the international accounting standards (IFRS) states that these adjustments have to be done in order to reflect the fair value of an OTC derivative. A short background and the derivation of CVA and DVA is presented, including related topics like various risk mitigation techniques, hedging of CVA, regulations etc.. Four different pricing frameworks are compared, two more sophisticated frameworks and two approximative approaches. The most complex framework includes an interest rate model in form of the LIBOR Market Model and a credit model in form of the Cox-Ingersoll- Ross model. In this framework, the impact of dependencies between credit and market risk factors (leading to wrong-way/right-way risk) and the dependence between the default time of different parties are investigated. / I den här uppsatsen har prissättning av motpartsrisk för en OTC ränteswap undersökts. Motpartsrisk kan definieras som risken att en motpart i ett finansiellt kontrakt inte har möjlighet eller viljan att fullfölja sin del av kontraktet. Motpartsrisken måste tas med I värderingen av ett OTC-derivat. Marknadspriset på motpartrisken är känt som Credit Value Adjustment (CVA). I ett bilateralt kontrakt, t.ex. som en swap, måste även den egna kreditvärdighet tas med i värderingen, vilket leder till en justering som är känd som Debit Value Adjustment (DVA). Sedan 2013 skall, enligt den internationella redovisningsstandarden (IFRS), dessa prisjusteringar göras vid redovisningen av värdet för ett OTC derivat. En kort bakgrund samt härledningen av CVA och DVA ar presenterade tillsammans med relaterade ämnen. Fyra olika metoder för att beräkna CVA har jämförts, två mer sofistikerade metoder och två approximativa metoder. I den mest avancerade metoden används en räntemodell i form av LIBOR Market Model samt en kreditmodell i form av en Cox-Ingersoll-Ross modell. I den här metoden undersöks även påverkan av CVA då det existerar beroenden mellan marknads