本論文研究如何建立一個投資組合用來追蹤穩定成長的目標線。我們將這個目標線追蹤問題建構成混合整數非線性數學規劃模型。由於用以追蹤目標線的投資組合，經過一段時間後其追蹤效能可能未如預期，本論文提出調整投資組合的數學規劃模型。這些模型中除了考量實務中的交易成本，亦考慮限制放空股票，所以將期貨加入投資組合中作為避險部位。最後，以台灣股票市場與期貨交易市場作為實證研究對象，探討投資組合建立與調整的表現，亦分析不同成長率設定之目標線與期貨投資比重上限對投資組合價值的影響。 / This thesis studies how to construct a tracking portfolio for the benchmark of a stable growth rate. This tracking problem can be formulated as a mixed-integer nonlinear programming model. Since the performance of the tracking portfolio may get worse when time elapses, this thesis proposes another mathematical programming model to rebalance the tracking portfolio. These models not only consider the transaction cost but also take into account of the limitation of shorting a stock; thus the tracking portfolio will include a futures position as a hedging position. Finally, an empirical study will be performed by using the data from the Taiwan stock market and the futures market to explore the performance of the proposed models. We will analyze how the different benchmark settings and the futures position limits will affect the value of the tracking portfolio.

本論文提出追蹤特定目標線的二階段混合整數非線性隨機規劃模型，以建立追蹤目標線的投資組合。藉由引進情境樹(scenario tree)，我們將此類二階段隨機規劃問題，轉換成為等價的非隨機規劃模型。在金融商品的價格波動及交互作用下，所建立的投資組合在經過一段時間後，其追蹤目標線的能力可能會日趨降低，所以本論文亦提出調整投資組合的規劃模型。為符合實務考量，本論文同時考慮交易成本、股票放空的限制，並且加入期貨進行避險。為了反應投資者的預期心理，也引進了選擇權及情境樹。最後，我們使用台灣股票市場、期貨交易市場及台指選擇權市場的資料進行實證研究，亦探討不同成長率設定之目標線與投資比例對於投資組合的影響。 / To construct a portfolio tracking specific target line, this thesis studies how to do it via two-stage stochastic mixed-integer nonlinear model. We introduce scenario tree to convert this stochastic model into an deterministic equivalent model. Under the volatility of price and the interaction of each financial derivatives, the performance of the tracking portfolio may get worse when time elapses, this thesis proposes another mathematical model to rebalance the tracking portfolio. These models consider the transactions cost and the limitation of shorting a stock, and the tracking portfolio will include a futures as a hedge position. To reflect the expectation of investors, we introduce scenario tree and also include a options as a hedge position. Finally, an empirical study will be performed by the data from Taiwan stock market, the futures market and the options market to explore the performance of the proposed models. We will analyze how the different benchmarks settings and invest ratio will affect the value of the tracking portfolio.

本論文含蓋三篇文章，分別從評價、避險和風險控管三方面，分析上限型股權連結保本票券。 第一篇文章為上限型股權連結保本票券之設計、評價和比較。本文考量投資人保守的投資行為與設限型股權連結票券所存在的delta跳躍(delta jump)現象，延伸Brennan and Schwartz (1976)模型，提出一個能在股價波動之際，使發行的避險部位delta呈現平滑變動且兼具保本(protected principal)功用的一般化模型(general form)。相較於一般的設限型股權連結保本模型，本模型具有以下特色。第一，加入股價成長率的調整因子(adjustable factor)，當景氣低靡，股價不停下跌時，正的調整因子可減緩股價下滑之勢，進而增加投資人在票券到期日時獲取更多資本利得(capital gain)的機會。同時，調整因子縮小了當期股價成長率與股價上限成長率(capped stock growth rate)之間的差距，繼而減緩delta 跳躍的幅度，降低發行者的避險成本。並且在HJM利率模型下，delta隨股價與股價波動度的變化更顯平滑(smooth)。第二，在保本率(protection rate)和參與率 (participation rate)不變之下，本模型的期初合理價格(fair price)較低，投資人能以較低的成本取得同等的投資保障。第三，若將本票券的名目面額(notional principal)視作共同基金(mutual fund)的淨值(net value)，而該淨值與股價連動，則本模型即成為股權連結的保本型基金(principal-protected fund)。 第二篇文章是路徑依賴之上限型股權連結保本模型之評價和風險測量。該文是擴展Brennan and Schwartz (1976)模型發展一個路徑依賴之上限型股權連結保本模型，並且提出一個比二元數模型更精確的封閉解。此外，也對七個時間序列進行股價波動度之精確檢定，得知AR-ARCH(1)模型對上限型股權連結保本票券而言，較其它時間序列模型，更能有效估計股價之波動度。 第二篇文章是外國資產的風險管理。目前在國內金融市場上，國外金融商品很多，大都以外幣計價，因此匯率風險是投資人不可忽視的因子。本文拓展Kupiec(1999)模型，將匯率風險加入模型中，使投資人更有效進行風險管理。 / This thesis studies valuation, hedge and risk management of capped equity-linked and principal-protected notes by means of the following essays: (1) Design, Valuation and Comparison of Capped Equity-linked and Principal-protected Notes (2) Valuation and Risk Measurement of Capped Equity-linked and Principal-protected Notes with Path Dependence (3) Risk Management of Foreign Assets Capped equity-linked and principal-protected notes are similar with barrier options. There exists delta jump as stock price or growth rate reaches the barrier. But previous studies about equity-linked and principal-protected notes with a restricted growth rate of stock price never explicitly discussed how the delta jump could be solved. In my first essay, I present a new design for capped equity-linked and principal-protected notes and add an adjustable factor to growth rate of stock price in such a way that the adjustable factor narrows the gap between the current stock growth rate and the capped stock growth rate and thus really reduces the magnitude of the delta jump and hence lowers the hedging cost for brokers. Recently, the focus of previous studies about principal-protected notes has been on either the restriction on the rate of stock return or the path dependence on the underlying asset, but not both in the same context. In my second essay, I develop a model on the capped, equity-linked and principal-protected notes with path dependence. There are two issues in this article. The first issue is valuation on the capped, equity-linked and principal-protected notes with path dependence. I find a closed-form approximation using the 2nd-order Taylor approximation and the method of Vorst (1992) that has higher accuracy than binomial tree model as maturity time or volatility becomes large. The second issue is risk measurement. I use VaR model to evaluate market risk of the principal-protected notes, and employ seven univariate time series models to forecast volatility and examine the accuracy. Additionally, investors may well encounter potential loss as the prices of financial products are reduced in the secondary market. The VaR is mainly concerned with the downside risk and becomes a standard measure of financial market risk that is increasingly used by investors. But if we want to apply 〝textbook〞formulation to risk management of foreign assets, there leaves exchange rate risk out of consideration. Therefore, I extend the work by Kupiec (1999) to present VaR formula with exchange rate risk for foreign assets and then to manage market risk usefully.

我國金融市場積極發展多元化與國際化，將由台灣期貨交易所推出臺指選擇權，建立選擇權市場以完備金融市場。由於選擇權市場掛牌交易契約眾多與選擇權的交易特性，因此有賴造市者發揮提供流動性、風險移轉、價格效率性及價格資訊揭露等經濟功能。本研究以造市者之功能性逐項比較我國造市者制度與EUREX、SEHK、LIFFE等各大交易所造市者制度之差異，用以發現我國首度引進的造市者制度對於選擇權市場發展的影響。 本研究為瞭解選擇權造市者營運的知識與技術，整理造市者作業循環的流程，針對造市者業務進行分工，建立起造市風險分析架構。推導得出造市風險包含造市交易風險與部位管理風險，呈現出市場波性風險、報價及交易策略風險、造市交易之市場機制風險、市場行情變動風險、遇險交易策略風險、部位管理之市場機制風險及財務與作業風險等七大類的造市風險。 本研究亦提出對於我國選擇權市場未來發展方向的關切，以及建議重視造市者利基與市場運作之關係，並提出未來與造市者相關之研究建議。 / Taiwan's financial market has been developing constructively into a globalization and multiplicity market within these years. To create a more completed financial market, Taiwan Futures Exchange (TAIFEX) will issue "the Taiwan stock index option" recently. As the complex and various features of the options trading, the option market will be successful and efficient through the market maker's economic functions, which are adding liquidity, increasing price efficiency, transferring risk and proving price information. This survey tried to compare the different functions of market maker system with TAIFEX, EUREX, SEHK and LEFFE, and to disclose the influence of the new market maker system on Taiwan's option market. This exposure takes great interest in market maker's knowledge and technology. By summarizing and classifying the operation process cycle flow of market maker, this research further organizes an analytic structure in market maker's risks. Including the market making risks and the positions management risks, the discussion demonstrates the market change risk, pricing strategy risk, limitary quoting risk, market volatility risk, hedging risk, mechanism risk, and finance and operation risk. The consequent also furnishes the concerns about the future development of Taiwan option market, emphasizing the importance of the relationship between market makers and market' benefit, and the suggestions to the further research.

美國次級房貸在1990年代中期曾經十分興盛，不過之後因LTCM危機，加上Fed採取連續升息政策，許多次級房貸放款的業者面臨資金流動性問題，以及次級房貸利潤不夠高，迫使許多業者退出這個市場，1998年亞洲金融風暴,美國雖未受波及,然自2000年開始因網路科技泡沫影响及2001年911恐怖攻擊,經濟衰退連續降息後，次級房貸在美國持續降息期間再度大幅成長，原因包括當時美國房價上升速度快、不動產市場流動性充裕，投資人增加對收益率較高產品的需求，導致更多次級房貸需求。 國際資金游動頻繁，衍生性產品及不動產證券化盛行，信用卡債、擔保債權憑證(CDO)、資產抵押證券被分割、包裝成證券或基金產品賣出，次級房貸風暴發生，間接亦影響到全球投資在上列產品之銀行、避險基金、機構法人、退休金等等…導致全球股票市場大跌，引發整個金融信用環境惡化，可能引發不良金融連鎖反應，從而導致更大的經濟金融危機。 美林證券、花旗銀行、歐美各大銀行相繼宣布資產減損,台灣國內銀行、保險公司亦陸續出現認列資產減損金額,只要一有次級房貸不利之消息出現,全球股市應聲而倒,截至目前問題所在雖略知一二,然國外金融業界因資訊較透明,其影響已漸公佈及擴大中,國內金融業則仍多採取保守態度,但亦逐漸依規定認列財產損失,然而問題是否已近尾聲,風險是否完全受控制則說法不一。 次級房貸問題的主要原因是相關金融商品證券化,層層包裝成各種衍生性產品,於次級房貸風暴發生後,信用風險連鎖反應造成相關產品無流動性,被隱藏的風險暴露後原有的信評機制幾乎全部失效,層層包裝的風險因事先未被定價,風暴後更無法估算其所會波及之影響,Mark to Market及34號公報迫使全球企業對次級房貸投資相關產品之損失提列資產減損,更加重各項產品流動性之停滯,信用危機造成信心危機，層層結構性產品及再轉投資,造成信用無虞的公司也遭魚池之殃,次級房貸衍生之金融商品,因主要購買者多為金融業或保險業或再包裝後出售予投資客,其後繼影響更是難以估計。 本論文內容除探討美國次級房貸定義、對美國國內及全球之影響、美國政府及各國政府的因應政策、截至目前影響及預計可能還會再出現影響,及因次級房貸之崩潰及衍生之金融產品之跌價所影響的層面與近年來國內外銀行爭相推展個人金融事業及財富管理事業的成立,是否有相當之關係,信用評等、風險控管、及定價在此風暴是否扮演重要角色,但卻又明顯失控?為避免類似情況再發生,應如何因應與防範?進而以提出個人對此事件探討之結論及省思後之建議。