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<p>Structured products are investment vehicles that combine basic financial instruments to provide private investors with packaged solutions to more advanced investment strategies in financial markets.</p><p>This paper investigates the pricing of 22 index-linked notes examined during their full life cycles between January 12, 2005 and January 17, 2007. The selected products constitute some 40% of the structured products issued by Swedbank in 2005, which at the time of the study is the second largest issuer of structured products to private investors in Sweden. Quoted prices on secondary markets are compared with duplication strategies using exchange traded options in order to calculate price differences.</p><p>The pricing results show that quoted prices deviate very little from their theoretical values in secondary markets. The price deviations are surprisingly low in an international comparison. Some indications have been found that the market maker is able to influence prices on secondary market by orienting the pricing towards the relative life cycle and moneyness of the structured products.</p><p>The importance of patterns in price deviations can, however, be questioned since the absolute level of pricing errors is low. There is little evidence to suspect that the issuer, Swedbank, systematically quotes prices that are not in line with their theoretical values. Sophisticated investors are thus likely to be able to judge the attractiveness of the structured product issue by comparing the transaction costs of the instruments in a duplication strategy with the transaction costs of the structured product. The author welcomes further research that includes multiple issuers to determine whether these findings apply for the Swedish market as a whole.</p>

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Structured products are investment vehicles that combine basic financial instruments to provide private investors with packaged solutions to more advanced investment strategies in financial markets. This paper investigates the pricing of 22 index-linked notes examined during their full life cycles between January 12, 2005 and January 17, 2007. The selected products constitute some 40% of the structured products issued by Swedbank in 2005, which at the time of the study is the second largest issuer of structured products to private investors in Sweden. Quoted prices on secondary markets are compared with duplication strategies using exchange traded options in order to calculate price differences. The pricing results show that quoted prices deviate very little from their theoretical values in secondary markets. The price deviations are surprisingly low in an international comparison. Some indications have been found that the market maker is able to influence prices on secondary market by orienting the pricing towards the relative life cycle and moneyness of the structured products. The importance of patterns in price deviations can, however, be questioned since the absolute level of pricing errors is low. There is little evidence to suspect that the issuer, Swedbank, systematically quotes prices that are not in line with their theoretical values. Sophisticated investors are thus likely to be able to judge the attractiveness of the structured product issue by comparing the transaction costs of the instruments in a duplication strategy with the transaction costs of the structured product. The author welcomes further research that includes multiple issuers to determine whether these findings apply for the Swedish market as a whole.

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.

本論文在Li(2000)的Gaussian Copula的背景之下，將資產價值服從常態分配的假設改為服從Variance Gamma分配，利用Copula模型模擬債權群組內各個標的資產的違約時點，並利用蒙地卡羅抽取亂數的方法，取平均之後求得信用連結債券所連結的資產債權組合價值。除此之外，本論文比較假設資產價值服從常態分配、Student t分配和Variance Gamma分配下，計算求得的資產池價值。實證結果顯示，假設服從Variance Gamma分配最接近市場的真實違約資料。這是由於Variance Gamma分配具備Student t分配的厚尾性質，能有效捕捉常態分配缺少的尾端損失機率，並可調整偏態係數和峰態係數，可以求出更接近市場價值的評價結果。最後，在敏感度分析方面，改變影響資產池價值的兩大因子：平均違約回收率和資產間相關係數。結果顯示，當平均違約回收率高於0.7時，相關係數越高的債權群組，其資產池價值亦越高。若平均違約回收率越低且資產間相關係數越高的話，越容易出現一起違約的現象，因此資產池價值會下降。因此投資人在挑選信用連結債券時，應注意所連結的標的資產群組內資產報酬的相關性，最好避免相關性高的資產群組，以免金融海嘯來臨的時候，多個資產同時違約的情形發生。

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狀況，使得原始信用風險債券在到期時的本金償付受到其他債券的信用風險影響，因此如何準確且客觀的估計資產池內違約機率便一個很重要的課題，而過去文獻常以給定參數的方式，並且假設資產間的違約狀況彼此獨立下進行評價，對於聯合違約機率的捕捉並不明顯，因此本文延伸Factor Copula模型，建立信用連結債券之評價模型，該模型考慮了資產間的違約相關程度，以期達到符合市場的效果，同時配合統計之因素分析法，試圖找出影響商品價格背後的市場因子。 本研究利用延伸的評價模型以及Copula法，對實際商品做一訂價探討，結果發現，不管是使用樣本內或樣本外的資料去評價時，本研究的評價模型表現都優於Copula法，表示說評價時額外加入市場因子的考慮，對於評價是有正向的幫助；而在因子選取方面，我們選取18項因子後，經由因素分析共可萃取出三大類因素，藉由觀察期望價格與市場報價的均方根誤差，發現國家因素以及產業因素均對於商品價格有所影響，而全球因素對於商品不但沒有顯著影響，同時加入後還會使得計算出的商品期望價格更偏離市場報價，代表說並不是盲目的加入許多因子就能使得模型計算出的價格貼近市場報價，則是要視加入的因子對於資產的影響程度而定。 對於後續研究的建議：由於本研究的實證中存在一些假設，使得評價過程中並不完全符合現實市場現況，若能得到市場上的真實數據，或是改以隨機的方式來計算，相信結果會更貼近市場報價；同時，藉由選取不同的因子來評價，希望能找出國家因素、產業因素以外的其他影響因子，可助於我們更了解此項商品背後的影響因素，使得投資人能藉由觀察市場因子數據來判斷商品未來價格走勢。 / Value of the credit-linked notes depend on the pool of assets whether default or not, so the promised payoff of credit-linked notes is affected by other risky underlying assets. Therefore, how to estimate the probability of default asset pool accurately and objectively will be a very important issue. In the past literature, researchers usually use given parameters, and assume assets probability of default are independent from each other under valuation. Furthermore, it is not obvious to capture the joint probability of default. Thus, this article extends the Factor Copula Model to provide a new methodology of pricing credit-linked notes, which consider the default correlation between the extent of assets in order to achieve result in line with market and with Factor Analysis method added, trying to figure out the impact of commodity price factor behind the market. In the empirical analysis, pricing the actual commodity issued by LB Baden-Wuerttemberg using extend model and Copula model, we found that no matter choose in-the-sample or out-the-sample data to valuation, the models in this article are superior to Copula model by compare the root-mean-square deviation(RMSE). It means add the market factors into our valuation is beneficial. In terms of selection factors, we select eighteen factors prepared by Morgan Stanley Capital International, and three categories of factors may be extracted from Factor Analysis method. By observing RMSE, both national factors and industry factors will influence on the commodity, but world factors not only did not significantly impact on the commodity, but also add it to calculate the expected price further from the market price. Representative said not blind join the many factors can make the model to calculate the price close to the market price, it is a factor depending on the degree of influence of the added asset. For the suggestion of future research. The fact that the presence of empirical assumptions in this study, result in the evaluation process is not entirely realistic to market situation. We suggest to get the real data on the market or use random way to calculate, we believe that the outcome will be closer to the market price. Meanwhile, by selecting different factors to evaluate, trying to discover further factors which significantly impact on the commodity; it will help us better to understand the factors behind the commodity, so investors can predict commodity future prices by observing the market data.

美國雷曼兄弟公司(Lehman Brothers Holdings Inc.)在2008年9月15日向美國法院申請破產保護，宣告進入美國破產法第11章重組程序，此程序影響由雷曼兄弟公司擔任發行或保證機構之連動債券。國內不少投資人購買雷曼兄弟相關的連動債券，因該等連動債券到期返還本金如係由雷曼兄弟公司支付或提供保證，當雷曼兄弟公司發生信用事件時，該公司之信用風險將可能導致該等債券之到期本金無法償付，造成投資人極度恐慌。 本研究從連動債券之發展、定義與類型出發，就投資人所爭議的銷售過程或資訊透明等議題，比較各國連動債券相關之法律規範，並就近年之國內外爭議案例進行法律分析，希望據以截長補短，並就我國在連動債銷售之法律規範之調整及紛爭解決機制等提出具體建議。

本文以目前台灣市場上所發行之兩個結構型商品—信用連動債券與利率連動債券為研究主題，信用連動債券之連動標的為國巨電子股份有限公司的信用風險，利率連動債券則以不同年限之交換利率利差為連動標的，本文利用數值方法分別評價此二理論價格，分析此類商品之結構、風險與收益。 本文以Hull and White利率三元樹模型和Li (1998) 建構信用曲線模型評價信用連動債券，並進一步分析信用模型內的回復率參數對信用連動債券價格之影響；在評價利率連動債券時，則採用LIBOR市場模型，利用蒙地卡羅模擬法模擬此商品之理論價格，並進行配息條款改變下之情境分析。

市場上為了因應投資人的需求，推出來越來越多樣化的結構式產品。結構型商品雖然標榜保本、高配息、高預期報酬，但仍然依照產品結構與連動標的不同，而有相當的投資風險。所以投資人應做好基本功課與認知，才能在投資連動債時明哲保身。 基於上述的理由，本文希望可以透過對結構式債券的評價、分析，讓投資人更了解投資結構式債券所面臨的風險與報酬，避免投資人因為不了解結構式債券的特性而遭受損失，或是因為不了解結構式債券而降低了投資的意願。 個案一為雙重結構利率債券，採用的評價方式為：先利用無套利Hull and White利率模型建構與市場式一致的利率期間結構，再搭配路徑函數的方式展出每日的利率樹，經過轉換後就可根據條款倒推求算利率連動債券的價格。 個案二為通貨膨脹連動信用債券：先採用Duffie and Singleton的方式建構信用曲線，求出違約邊際機率後；再透過Monte Carlo的方式模擬消費者物價指數來計算每期配息。在已知每個節點的預期現金流量後，就可利用倒推的方式求解信用連動債券的價格。