傳統上描述利率期間結構，不外乎藉由瞬間短期利率的隨機過程（如：Hull and White模型），或瞬間遠期利率的隨機過程（如：HJM模型）。應用這些方式理論上雖然可行，但是市場上並無法觀察得知這些瞬間利率。 Brace-Gatarek-Musiela利率模型（簡稱BGM模型）是將HJM模型間斷化，直接推導市場上可觀察得到之LIBOR利率的隨機過程，用它來描述市場利率期間結構，並利用數學的技巧，推導出符合對數常態的型式，方便使用Black公式來求解，且同時考慮LIBOR利率之波動程度，透過與市場資料的校準，符合市場上的利率期間結構及利率波動結構，有助於利率衍生性商品的訂價與避險。 由於市場上有愈來愈多的利率衍生性商品，不是由單純的cap、swaption來組成，例如：路徑相依選擇權、美式選擇權、回顧型選擇權…等，這些新奇選擇權要求出評價公式很難，所以通常使用數值方法來評價。常用的數值方法有蒙地卡羅模擬法及樹狀圖評價法，由於使用蒙地卡羅模擬法處理起來較耗時，而且評價美式選擇權比較麻煩，而樹狀圖評價法較省時，且應用較廣。因此，本文除了詳細推導BGM利率模型，並建構出BGM利率模型下的利率樹，來對這些新奇選擇權做評價。 最後做一實證分析，以市場上的所發行的利率連動債券為例，對於匯豐銀行美元護本109利率連動債券的設計、評價、損益分析及其相關議題做詳盡的探討。

在中國金融市場逐步開放，結構型理財商品的發行與需求日益增加的情形下，本文以目前市場上已發行的利率連結商品與匯率連結商品為個案，進行評價與分析。在利率連結商品方面，以連結6個月美元LIBOR利率的「美元12個月期逆浮動利率連動債」為例，採用Brace, Gaterek and Musiela（1997）提出的LIBOR市場模型（又稱BGM模型），由市場觀察到的即期LIBOR利率與交換利率，求出遠期利率的起始值，並利用市場上利率上限選擇權（CAP）報價，校準遠期利率波動度結構，而遠期利率間的相關係數矩陣則以歷史資料來估計，然後以蒙地卡羅模擬法進行商品評價；在匯率連結商品方面，以連結日元兌澳元、英鎊、歐元匯率的「美元三個月期組合匯率理財專案」為例，採用Garman and Kohlhagen（1983）外匯選擇權的匯率動態過程，利用歷史資料求出各匯率變動率波動度以及各匯率間的相關係數矩陣，然後以蒙地卡羅模擬法進行商品評價。此外亦針對兩種商品的敏感性與避險參數作分析，最後分別由發行商與投資人的觀點，探討其發行與投資該商品的策略與風險所在。

隨著中國人民所得增加，政府實施金融改革，中國理財產品市場愈來愈蓬勃發展，產品種類繁多，投資人可選擇的產品種類相對增加，但如何從令人眼花撩亂的產品中選擇適合自己且可獲得利潤的產品是相當重要的。 本文針對中國已發行之理財產品進行評價與分析，首先採用蒙地卡羅模擬法評價招商銀行發行之“金葵花”08中國系列之行業領袖港幣理財計劃，本產品是股權連動商品。接著以LFM利率模型評價與分析中國銀行發行之0501B美元聚寶盆理財產品。分別模擬出產品的理論價格，最後針對評價的結果探討發行商之發行策略及投資人所面臨的風險。

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.

<p>Takeover is a business activity which really started in the beginning of the eighties and which still takes a strong part in the business and financial area all over the world. According to our studies as the desire for further acknowledgements and the desire of building a career around financial activities, this study has been naturally conducted in the banking area.</p><p>Regarding the steady use of acquisition like a powerful process with some positive and negative sides, we decided to implement a comparison of different mergers and acquisitions in the banking industry in the United States and Europe. This comparison has been supported and based on the third main topic of our study: performance.</p><p>These large and complex subjects combined together lead to the following hypotheses:</p><p>Hypothesis 1: Performance is not improved after takeover in the banking industry.</p><p>Hypothesis 2: The level of post takeover performance is the same in the U.S. as in the European bank acquisitions.</p><p>Based on the historical data and knowledge, the United States was the pioneer in the development of such gathers in the banking sector. Considering the United States as a reference, a first purpose was to compare them with the bank mergers and acquisitions in Europe. Stating on some possible differences as increasing our own knowledge have been some others purposes which have supported our work.</p><p>A first large part of our work was focused, through a large literature review, on the enhancement of our knowledge as the statements of the basis and support for the analysis.</p><p>To illustrate and to try to answer our research question, we have conducted our study based on a sample of 20 acquisitions which were achieved in the banking industry between March 1998 and May 2004. 10 of these acquisitions had been achieved in the United States as the 10 remaining acquisitions had been executed in Europe.</p><p>The analysis has been achieved by collecting data in Thomson Datastream Advance.</p><p>Based on a quantitative method, we applied two financial models: The Market Model (MM) and the Market-Adjusted Returns Model (MAR) supported by the Cumulative Abnormal Returns Method (CARs).</p><p>The post-takeover study has been delimited on a period of 42 months after the public announcement.</p><p>The study and the comparison between the United States and Europe have shown some differences between the two areas. Nevertheless it seems that negative abnormal returns are usually the case after such takeovers on the whole period studied. Some positive abnormal returns have been recorded at different points in the time into the studying period.</p><p>According to the models we applied, the US banks results seem to be better than the ones of European banks: the differences range from 5,58 to 16,65 points under the MM, and from 1,66 to 18,08 points under the MAR model.</p>

Takeover is a business activity which really started in the beginning of the eighties and which still takes a strong part in the business and financial area all over the world. According to our studies as the desire for further acknowledgements and the desire of building a career around financial activities, this study has been naturally conducted in the banking area. Regarding the steady use of acquisition like a powerful process with some positive and negative sides, we decided to implement a comparison of different mergers and acquisitions in the banking industry in the United States and Europe. This comparison has been supported and based on the third main topic of our study: performance. These large and complex subjects combined together lead to the following hypotheses: Hypothesis 1: Performance is not improved after takeover in the banking industry. Hypothesis 2: The level of post takeover performance is the same in the U.S. as in the European bank acquisitions. Based on the historical data and knowledge, the United States was the pioneer in the development of such gathers in the banking sector. Considering the United States as a reference, a first purpose was to compare them with the bank mergers and acquisitions in Europe. Stating on some possible differences as increasing our own knowledge have been some others purposes which have supported our work. A first large part of our work was focused, through a large literature review, on the enhancement of our knowledge as the statements of the basis and support for the analysis. To illustrate and to try to answer our research question, we have conducted our study based on a sample of 20 acquisitions which were achieved in the banking industry between March 1998 and May 2004. 10 of these acquisitions had been achieved in the United States as the 10 remaining acquisitions had been executed in Europe. The analysis has been achieved by collecting data in Thomson Datastream Advance. Based on a quantitative method, we applied two financial models: The Market Model (MM) and the Market-Adjusted Returns Model (MAR) supported by the Cumulative Abnormal Returns Method (CARs). The post-takeover study has been delimited on a period of 42 months after the public announcement. The study and the comparison between the United States and Europe have shown some differences between the two areas. Nevertheless it seems that negative abnormal returns are usually the case after such takeovers on the whole period studied. Some positive abnormal returns have been recorded at different points in the time into the studying period. According to the models we applied, the US banks results seem to be better than the ones of European banks: the differences range from 5,58 to 16,65 points under the MM, and from 1,66 to 18,08 points under the MAR model.

The selection of investment strategies and managing investment funds via employing portfolio insurance methods play an important role in asset liability management. Insurance strategies are designed to limit downside risk of portfolio while allowing some participation in potential gain of upside markets. In this thesis, we provide an extensive overview and investigation, particularly on the two most prominent portfolio insurance strategies: the Constant Proportion Portfolio Insurance (CPPI) and the Option-Based Portfolio Insurance (OBPI). The aim of the thesis is to examine, analyze and compare the portfolio insurance strategies in terms of their performances at maturity, via some of their statistical and dynamical properties, and of their optimality over the maximization of expected utility criterion. This thesis presents the financial market model in continuous-time containing no arbitrage opportunies, the CPPI and OBPI strategies with definitions and properties, and the analysis of these strategies in terms of comparing their performances at maturity, of their statistical properties and of their dynamical behaviour and sensitivities to the key parameters during the investment period as well as at the terminal date, with both formulations and simulations. Therefore, we investigate and compare optimal portfolio strategies which maximize the expected utility criterion. As a contribution on the optimality results existing in the literature, an extended study is provided by proving the existence and uniqueness of the appropriate number of shares invested in the unconstrained allocation in a wider interval.