本研究針對保本型變額壽險－投資標的為債券型基金進行進行評價分析。由於投資型保險擁有投資與保障的功能，且將投資風險轉嫁給投保人，與傳統壽險有明顯的差異。爲防止投保人承受過多的投資風險而失去保險中保障的功能，在條款中加上一最低保證給付金額，使投保人只須負擔部分的投資風險，保險公司也可提升其產品競爭力。 在保本型變額壽險的評價模型上，運用精算數學中收支相等原則，採用Nielsen and Sandmann(1995)的模型架構求算合理保費。同時採用利率模型－BGM Model，透過市場可觀察到的LOBOR報價，更精確有效地對利率期間結構進行模擬分析。再針對死亡保險及生死合險，兩種目前國內壽險市場上的主流商品，探討在分期繳費方式下的合理保費。 最後，因為此模型不存在封閉解，透過蒙地卡羅法進行數值模擬，針對參數可能的變動進行敏感度分析。

The main goal of this thesis is to suggest an appropriate approach to interest rate risk modeling in the Czech financial market environment in various situations. Three distinct periods are analyzed. These periods, which are the period before the global financial crisis, period during the financial crisis and in the aftermath of the global financial crisis and calming subsequent debt crisis in the eurozone, are characterized by different evaluation of liquidity and credit risk, different relationship between financial variables and market participants and different degree of market regulations. Within this goal, an application of the BGM model in the Czech financial market environment is crucial. Use of the BGM model for the purpose of predicting a dynamics of a yield curve is not very common. This is firstly due to the fact that primary use of this model is a valuation of interest rate derivatives while ensuring the absence of arbitrage and secondly its application is relatively difficult. Nevertheless, I apply the BGM model to obtain predictions of the probability distributions of interest rates in the Czech and eurozone market environment, because its complexity, direct modeling of a yield curve based on market rates and especially a possibility of parameter estimation based on current swaptions volatilities quotations may lead to a significant improvement of predictions. This improvement was also confirmed in this thesis. Use of swaptions volatilities market quotations is especially useful in the period of unprecedented mone- tary easing and increased number of central banks and other regulators interventions into financial markets that occur after the financial crisis, because it reflects current market expectations which also include future interventions. As a consequence of underdevelopment of the Czech financial market there are no market quotations of Czech koruna denominated swaptions volatilities. I suggest their approximations based on quotations of euro denominated swaptions volatilities and also using volatilities of koruna and euro forward rates. Use of this approach ensures that predictions of the Czech yield curve dynamics contain current market expectations. To my knowledge, any other author has not presented similar application of the BGM model in the Czech financial market environment. In this thesis I further predict a Czech and Euro area money market yield curve dynamics using the CIR and the GP models as representatives of various types of interest rates models to compare these predictions with BGM predictions. I suggest a comprehensive system of three criteria, based on comparison of predicti- ons with reality, to describe a predictive power of selected models and an appropria- teness of their use in the Czech market environment during different situations in the market. This analysis shows that predictions of the Czech money market yield curve dynamics based on the BGM model demonstrate high predictive power and the best 8 quality in comparison with other models. GP model also produces relatively good qua- lity predictions. Conversely, predictions based on the CIR model as a representative of short rate model family completely failed when describing reality. In a situation when the economy allows negative rates and there is simultaneously a significant likelihood of their implementation, I recommend to obtain predictions of Czech money market yield curve dynamics using GP model which allows existence of negative interest rates. This analysis also contains a statistical test for validating the predictive power of each model and information on other tests. Berkowitz test rejects a hypothesis of accurate predictions for each model. However, this fact is common in real data testing even when using relatively good model. This fact is especially caused by difficult fulfilment of test conditions in real world. To my knowledge, such an analysis of the predictive power of selected interest rate models moreover in the Czech financial market environment has not been published yet. The last goal of this thesis is to suggest an appropriate approach to obtaining pre- dictions of Czech government bonds risk premium dynamics. I define this risk premium as a difference between government bond yields and fixed rate of CZK IRS with the same length. I apply the GP model to describe the dynamics of this indicator of the Czech Republic credit risk. In order to obtain a time series of the risk premium which are necessary for estimation of GP model parameters I firstly estimate yield curves of Czech government bonds using Svensson model for each trading day since 2005. Resulting si- mulations of risk premium show that the GP model predicts the real development of risk premiums of all maturities relatively well. Hence, the proposed approach is suitable for modeling of Czech Republic credit risk based on the use of information extracted from financial markets. I have not registered proposed approach to risk premium modeling moreover in the Czech financial market environment in other publications.

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。

目前中國大陸金融市場伴隨著經濟體日趨成熟與影響力的情形之下，已逐漸開放，結構型理財產品多元化發展，使中國大陸的衍生性商品市場越趨活躍，相繼陸續開放承作各類型的金融商品，金融市場更加完備。不論是發行商或是投資人，皆應更深入了解結構型理財產品，才有助於中國大陸衍生性商品市場的拓展。 本文針對中國大陸金融市場上已發行的股票掛鈎型與利率掛鈎型的結構型理財產品進行個案評價與風險分析，第一個評價個案為「追蹤能源類股股權掛鈎結構型理財產品」，以封閉解作為評價基礎，並採用蒙地卡羅法模擬本商品的提前到期機率；第二個評價個案為「每日計息雙區間可贖回結構型理財產品」，採用BGM模型進行評價，並利用最小平方蒙地卡羅模擬法，考慮發行商提前贖回條款並計算每一期的配息；分別對兩個個案進行評價，針對評價結果分析發行商的利潤與避險策略，並給予投資人投資與避險的建議。

本文分別評價了中國大陸地區發行之利率結構型商品及股權結構型商品，並針對其風險及條款設計進行分析。文中所選的利率結構型商品為「每日計息利率連動理財產品」，在對數常態遠期LIBOR模型的假設下，我們先利用市場報價校準參數化之波動度及相關係數函數，再使用最小平方法蒙地卡羅模擬利率路徑，以處理此商品的提前贖回條件；為了產生非標準期間之遠期LIBOR利率，在模擬過程中加入了Brigo和Mercurio(2006)提到的漂移項插補法。另一個股權結構型商品為「人民幣A股多資產連結理財產品」，由於此商品連結標的多達五個，本文中使用風險中立下股價的動態過程，以及蒙地卡羅模擬來求算其合理價格。此外，針對這兩個商品所需要注意的風險，本文皆提出了建議。

隨著低利率時代的來臨，投資人不能再從定存或證券中獲取高報酬率，在另一方面，許多的結構型商品相繼出現，如高收益票券、投資型定存、投資型保單等，打著高收益的稱號來吸引市場上的投資人購買。但是許多投資人持有負面的見解，認為此種商品並非無風險，甚至時常出現血本無歸的情形，究竟投資人如何在眾多商品中選擇出最有利的商品？另外，近年來金融業的商品朝向國際化與多元化發展，但是國內銀行及券商能夠承作金融商品創新及設計有限，不僅無法滿足國內投資人，對於證券商與銀行業來說也有不利的影響，因此健全結構型商品的發展才能使得金融業，證券商與一般投資人三贏的局面。 / 本文分別評價了ING銀行發行之利率結構型商品及元大證券之股權結構型商品，並針對其風險及條款設計進行分析。文中所選的利率結構型商品為「ING五年期目標贖回連動債券」，在對數常態遠期LIBOR模型的假設下，我們先利用市場報價校準參數化之波動度及相關係數函數，再使用最小平方法蒙地卡羅模擬利率路徑，以處理此商品的提前贖回條件。另一個股權結構型商品為「「絕對保富」結構型商品」，由於此商品連結標的多達三個，本文中使用風險中立下股價的動態過程，以及蒙地卡羅模擬來求算其合理價格。此外，針對這兩個商品所需要注意的風險，本文皆提出了建議。

本文分別評價了美元交換利率連結之結構型商品及在香港發行的一檔股權結構型商品，並針對其風險、報酬及條款設計進行分析與建議。文中所評價的利率結構型商品為「11倍利差連動債券」，在對數常態遠期LIBOR模型(LFM)的假設下，我們先利用市場報價的Swaption求出期初的殖利率，再以殖利率求算期初的遠期利率。而交換利率可由一連串的遠期LIBOR利率計算出來，模擬之前我們還需先校準模型的波動度函數及相關係數函數，再使用最小平方法蒙地卡羅模擬利率路徑，以處理此商品的提前贖回條件。另一個股權結構型商品為「Fortune Accumulator」，假設股價變動皆符合幾何布朗運動(Geometric Brownian Motion)，並且在風險中立的條件下，其動態過程可經由Ito’s Process轉換出其股價路徑，再利用蒙地卡羅模擬來求算其合理價格。

本文分別評價了目前市面上最常見的利率連動與股權連動之結構型商品，並針對其風險及條款設計進行分析。文中所選擇的利率結構型商品為「10年期長短期利差型連動債券」，在對數常態遠期LIBOR模型（LFM）的假設下，首先利用市場報價校準參數化之波動度及相關係數函數，再使用最小平方法蒙地卡羅模擬利率路徑，以處理此商品的提前贖回條件。另一個股權結構型商品為「美日爭鋒連動債」，由於此商品包含S&P500與Nikkei225兩個連結標的指數，文中針對兩指數套用不同的參數以利後續的蒙地卡羅模擬之進行，並依此求算其合理價格。文末，針對此兩商品所必須注意的風險，本文亦提出了建議。

2008年初，正值美國籠罩次級房貸風暴影響、全球經濟景氣趨緩、產油國地緣政治因素造成能源價格創新高…等險峻經濟狀況之際，投資銀行設計一包含 :搭配出局條款之CMS Spread雪球型利率結構商品及結合附加WTI上限、USD/JPY匯率上下限之異型選擇權的混合結構性商品提案。本文依據標的資產屬性，參考相關文獻及近期在頂級期刊發表之利率資產評價模型研究中，選用Extended BGM模型(Ting-Pin Wu, and Son-Nan Chen(2007))、遠期曲線模型及匯率評價模型為個案之基礎評價模型；以無套利觀念依取得之市場各資產相關公開報價資料估算各模型所需之參數；由於屬於雪球利率結構型商品及路徑相關特性，在目前相關文獻無封閉解的條件下，使用蒙地卡羅模擬獲得未來各資產之現金流折現值，進而計算預期理論價值。依據上述方法論評價所獲得之預期理論價格顯示，個案並非具公平價值之交易，依此結論強烈建議客戶不應該承做本交易。 個案相當於投資銀行以買入一個5年期附帶出局條件，隱含看空經濟景氣循環之CMS Spread選擇權及買入一個1年期看空WTI價格選擇權建構此混合結構性商品。為強化客戶承做意願，設立一似乎觸及機會很大，但從交易後至今從未觸及的出局條件，又透過每日數位選擇權計息方式將WTI波動度資產化，提供大於10%之相對LIBOR rate 很高，但實際是被低估之半年收息固定費率。由於雪球型利率結構型商品特性，收益不僅取決於是否達成交易付款條件，更重要因素是達成時間點之速度。 在蒙地卡羅模擬資產價格路徑中，觸及頭一次CMS Spread付款條件天數之眾數區間為125至135，貼近實際136天。從評價結果，交易之付款條件內已隱含透過兩個不同標的資產選擇權之高預期獲利相互達到避險、套利及強化收益等效益;投資銀行可以不用額外對受眾多複雜不確定因數影響之WTI價格採取避險策略，而將所有避險成本轉嫁於選擇權賣方的客戶。在資本計提規範下及確保未來預期收益之考量下，投資銀行唯一要做是以低成本尋求中介銀行進行背對背交易以強化因市場風險所衍生之信用風險。 從研究過程，不禁讚嘆個案是投資銀行設計建構在財務工程科學上的卓越藝術及策略，從它一旦出現世界上之瞬間，個人預估其價值將達34,211,458.09美元! / Early 2008 was a steep economic era when U.S. was enveloped by subprimemortgage crisis, world's economy was slowing down, and energy prices were pushed to a historical record high by oil geopolitical factors. Under this situation, an investmentbank designed a hybrid structure product, which includes a CMS Spread Snowball interest rate structured product with USD/JPY FX rate Knock out condition, a WTIoption of an additional upper limit, a USD/JPY exchange rate combined exotic option of upper and lower limits. After considering assets attributes and reviewing the relevant literature and recent research published in top journals related to the interest rate assetpricing model, Extended BGM model (Ting-Pin Wu, and Son-Nan Chen (2007)), forward curve model, and FX Rate model are selected as the basic pricing models. Tocalculate the expected theoretical value of this structured product, the unavailable model parameters of assets are estimated through the public market data based on thearbitrage-free concept, and the discounted values of the assets future cash flows are obtained by Monte Carlo simulation because of snowball interest rate structured product and path dependency characteristic and no close form solution in current relevant literature. The results of the pricing models shows that the net present value(NPV) received by customers is lower than that received by the investment bank, theconclusion is : Strongly recommend customers should not to do this trade ! In this case, the investment bank used a long position of one 5-year period CMSSpread Option with knock out condition, which implies Bearish on the economic cycle, and a short position of a 1-year period WTI option with up and low limits condition to construct this hybrid structure product. To draw customers’ attention to this proposal, the investment bank designed a knock out condition that seemed to be met very easily,but the price never touched by the article finished date. Additionally, a daily accrued digital option is used to transfer WTI volatility to a semi-annual fixed yield over 10% that, compared to LIBOR Rate, is very high but actually is underestimated. For theSnowball structure product, the total profit depends on not only when but also, more importantly, how soon to meet the payment condition. According to the asset pricing path generated by Monte Carlo simulation, the mode range which CMS Spread payment condition first met is 125 to 135 days after the contract’s value date, very close to the actually history data of 136 days. From pricing results, terms of contract implied that two different options combined to hedge risk and gain profit from each other. Hence, the investment bank does not need to make extrahedge strategy to WTI price which is impacted by more complicated risk factors.However, customer must spend hedge cost because of taking much risk as a sell option role. Under the Capital Charge regulation, to lock up the expected profit, what the investment bank needs to do is only to pay a very low cost fee, which like insurancepremium, to look for an intermediary bank to offer a back to back trade to manage thecredit risk caused by market risk! During the research of this paper, I am amazed what an excellent art and strategy that designed by the investment bank based on financial engineering science! As this structure product appeared in this world, I estimated that it would worth 34,211,458.09 USD.

在過去二到三年之中，能源、金屬、軟性商品等原物料價格漲勢強勁，成為市場上最炙手可熱的商品。然而，原物料價格漲升為全球帶來了通膨隱憂，世界各國紛紛採用各種貨幣政策和財政政策試圖緩解通膨壓力。其中，利率政策即是相當重要的一環。在這樣的背景之下，是否對於能源、貴金屬和利率衍生性商品的設計和定價上產生影響，值得進一步檢視。因此，本論文選擇以中國大陸的原油與黃金連結複合式選擇權，以及利率（HIBOR）連結可贖回每日區間計息等兩種結構性存款作為研究個案，以財務工程的理論模型為中國銀行的金融創新產品作評價與分析。 在原油與黃金連結複合式選擇權部分，分別假設金價和油價服從幾何布朗運動（Geometric Brownian Motion）推導出封閉解，以及Schwartz的一因子均數回歸模型，採蒙地卡羅模擬法模擬標的資產之價格路徑並以之估算商品理論價值和發行機構利潤，之後則就避險參數和商品預期收益率作分析。在利率連結可贖回每日區間計息結構性存款部分，由於具有發行機構可提前贖回的特性，本論文採用LIBOR市場模型（BGM Model）為評價基礎，先利用市場報價資訊計算期初遠期利率及進行參數校準，再以蒙地卡羅模擬法模擬遠期利率路徑，最後以Longstaff and Schwartz（2001）提出的最小平方蒙地卡羅法（LSM）計算商品理論價值和發行機構利潤。 除估算商品理論價值以檢視中國銀行的商品定價合理性之外，本文也針對中國大陸的外匯和利率政策對金融機構在商品設計方面的影響作分析，最後則分別就財務工程與金融創新以及總體政策與金融市場兩方面提出結論與建議，以供各界參酌。 / The prices of physical commodities have risen a lot and led to pressure of inflation for several years. Many countries over the world have tried hard to tackle inflation threat with monetary and fiscal policies. Under this circumstance, the design and pricing of structured products should be affected. Therefore, the oil and gold-linked and interest rate-linked structured deposits launched by Bank of China are selected to be the case study in this thesis. Prices of the underlying assets are assumed to follow Geometric Brownian Motion, and the close-form solution of the oil and gold-linked structured deposit embedded with compound options is derived. Moreover, Schwartz’s One-Factor Mean Reversion Model is adopted to derive the fair value by simulation. In addition to the fair value and issuer’s profit, the expected rate of return, hedge parameters (Greeks) and model difference are presented in this thesis. As for the interest rate-linked Callable Daily Range Accrual Deposit, the thesis presents the steps of pricing by simulation. LIBOR Market Model (BGM Model) is adopted to derive the fair value of Callable Range Deposit with Least Squares Monte Carlo approach. Besides, the design and pricing of structured products are actually influenced by those policies in relation to interest rates and currencies adopted by government of Mainland China. The influence is discussed in the thesis as well. Eventually, the conclusions and suggestions are made with respect to macroeconomic policy and financial market as well as financial innovation.