由於電腦革命的成功，在短暫的幾年之間，更加速了經濟的成長，而金融的投資分析，是社會經濟發展的原動力，因此研究這方向的財務數學也相對的提高了專家、學者的研究熱潮。就以股票、匯率市場來說，如果能比别人早一步掌握行情走勢，就能獲得較高的利潤。但影響股價、匯率波動的因素很多，尤其是在複雜多變及不確定性的資訊下。因此；如何進行更精確的趨勢分析與預測，是本文研究的主題。由於，傳統的期望值是二元的邏輯思考(非1即0)，比較無法符合多變與不確定的財金問題，因此本文考慮以模糊統計方法，以模糊期望值的方法來作趨勢分析與預測，期望能對複雜多變的財金體系提共一套更精確合理的投資分析方法，可以提供投資者更多的訊息，做出明確的抉擇。最後；以我國集中市場加權股票指數、台幣對美元匯率及台積電股價為例，做一實例上的詳細探討。 / Based on computer revolutionary coming off, economics grows fast in previous several years, then the investment analyze of finance is the impetus of development of society economic. Therefore, many experts and scholars are interested in the research of financial mathematics. Taking stock market and exchange market for example, if you can predict the future trend of market, you obtain more profit. However, there are many factors that act on stock prices and exchange rate. Especially, the market information is complicated and incomplete. How to go along accurate trend analysis and divination is the important point of the text research. Because traditional expectation value is dibasic logic thought (either 1 or 0), that can’t conform to the highly changeable and uncertain finance problems. For this reason, in this research we propose an integrated procedure for fuzzy expectation value modeling and forecasting through fuzzy relation equations. We apply this technique to construct a fuzzy expectation value model for Taiwan Weighted Stock Index and exchange rate and forecast future trend. We strongly believe that this model will be profound of meaning in forecasting future trend of financial market.

本論文主要結合了「匯率連動選擇權」與「多點重設型選擇權」、「履約價回顧型選擇權」，除了評價與分析四款匯率連動多點重設型賣權以及匯率連動履約價回顧型賣權，並且探討重設點之選擇對於賣權價格之影響，使其理論與模型更為一般化，發行券商或銀行欲發行此類商品時，更能夠依據模型做更進一步之風險控管，藉以降低避險損失。 / For the most part, this article combines the quanto option with the multiple-reset put and lookback put. In addition to price and analyze the four specific types of quanto multiple-reset puts and quanto lookback puts, this article also provides a more comprehensive study on how the frequency of resetting in exercise price affects the quanto puts’ price and risk. When issuers issue this kind of financial product, based on the model in this article, they will be able to better control the risk further and secure the investment return by diminishing the loss of hedging.

無 / This study investigates the monetary effects under the floating exchange rates and imperfect capital mobility by extending the model of Bernanke and Blinder (1988) into a small open economy. It is shown that with credit channel of monetary transmission explicitly considered, the effect of monetary policy on output may be augmented or lessen in our model depending on whether the exchange rate depreciates or appreciates. In addition, the exchange rate puzzle found in the empirical studies can be explained in our theoretical model. The dynamic adjustment patterns of the output and the exchange rate after an increase in money supply are further examined. Under the case of relative high capital mobility, when the real output gradually adjusts toward a higher level, the exchange rate may overshoot, undershoot, or even counter-shoot during the dynamic adjustment process. This provides another one explanation for the volatility of exchange rates under floating rates. Therefore, as financial markets become more internationalized, the conduct of monetary policy turns more complicated in an open economy.

本論文主要是以實質選擇權分析法對在最適決策下供應鏈及公司的價值進行評價。內容包含兩篇文章。第一章為緒論；第二章與第三章為主文。在此兩章中 ，我們會先介紹研究動機、目的與文獻探討，接著架構模型，據以求出於最適決策下供應鏈或公司價值的封閉解後，以比較靜態分析法分析各參數對供應鏈或公司價值的影響。第四章為總結。 / 第一篇文章為對在隨機成本下供應鏈的評價。該模型是以單一供應商、單一零售商與多個消費者組成之垂直整合的二階段序列式動態供應鏈為架構，假設市場的現貨價格為動態過程，供應商和零售商每單位商品的成本為隨現貨價格變動的隨機成本。在此模型中，供應鏈的經營者以銷售量為決策，聯合利潤最大化為目標。此外，存貨設定在零售商的一方，而零售商所持有的存貨可視為擁有一個無窮期的美式買權，當存貨出清時，如同執行一個美式買權一般，以促使利潤的實現。接著我們利用比較靜態分析法就無風險利率和現貨價格報酬率的波動度對於最適決策下所求得的供應鏈價值之影響進行分析後，得到供應鏈價值會隨著無風險利率的上升而增加，亦會隨著現貨價格報酬率波動度的提高而增加。此結論和Cortazar and Schwartz(1993)以兩階段製造產品為運作模式之公司價值就無風險利率和現貨價格報酬率的波動度進行比較靜態分析後所得到的結果一致。 / 第二篇文章為對在隨機匯率下兩階段生產之公司進行評價。此文考慮Cortazar and Schwartz(1993)的模型，在產品之製造為兩階段式生產的條件下，納入隨機匯率，用實質選擇權分析法，評價以外銷專案為標的之公司價值。我們針對模型中的參數：本國的無風險利率、以外幣計價之現貨價格報酬率波動度及匯率波動度的變化對公司價值的影響進行分析後，而得到這些參數與公司價值呈現正相關的結果。此外，因動態現貨價格與隨機匯率的相關性 ，我們亦分析現貨價格和匯率的相關係數對公司價值之影響後，得到兩者正相關程度越大或是負相關程度越小時，公司價值就越大，從而體認到僅從匯率走勢的升值或貶值來判斷外銷專案價值有利與否是不夠詳盡的，還要考慮現貨價格和匯率交互影響的程度，決策者才能做出有利於外銷專案更好的決定。 / 最後，我們將此兩篇文章歸納出一些重要的結論後，接著針對本論文研究主題的未來發展方向，提出一些觀點和建議，以作一個總結。 / This text uses a real options approach to price the value of the supply chain or the company. It contains two articles . Chapter 1 is the introduction; Chapter 2 and Chapter 3 are the main text.In these chapters, we introduce the study motive and literature review, the model, the closed form of the supply chain or the company in the optimal operating policy, and then use comparative statics method to analyze the effect of some parameters that risk-free interest rate, volatility of the spot price, volatility of the exchange rate etc. Finally, we give a summary. / The first article is in Chapter 2. It is to price the optimal value of the two echelon sequential dynamic supply chain which is composed of one supplier, one retailer and many consumers. In this model, we assume that the spot price of goods is a dynamic process, the costs of the per unit goods of supplier and retailer are up to the change of the spot price, the sales volume is the decision strategy, and their aim is to maximize joint profits. In this supply chain, the value of the stocks for retailer can be regarded as a perpetual American call option. Finally, we will use comparative static to examine the effect of the volatility of the spot price and risk free rate for the optimal value of the supply chain, and we obtain the same results as Cortazar and Schwartz’s (1993) optimal value of two-stage companies. / The second article is in Chapter 3. Based on the extended the Cortazar and Schwartz (1993) model, we use the Real Options Approach to price the closed form of the value of the two-stage production for a company under stochastic exchange rate. With regard to the parameters in the model: domestic risk-free interest rate, the volatility of the foreign spot price, and the volatility of the exchange rate, we find that the domestic risk-free interest rate, volatility of the foreign spot price, and the volatility of exchange rate have positive correlated with the optimal value of the company. Moreover, due to the correlated relation between the dynamic foreign spot price and the stochastic exchange rate, we analyze the change of the coefficient of correlation between the foreign spot price and the exchange rate, and obtained the more large optimal value of the company when they are more large positive correlated or negative correlated. In other word, we need to consider the influence between the foreign spot rate and the exchange rate at the same time, and then the manager can make the optimal decision about the exporting project. / Finally, we summed up some important conclusions of Chapter 2 and Chapter 3, and then proposed some views and suggestions for the study the theme and the developing direction in the future.

近年來，中國的經濟表現受眾人稱羨之餘，實質固定匯率政策卻為人所詬病。然而，中國人民銀行於 2005 年 7 月 21 日公告一套以市場供需為基準的管理浮動匯率制度後，人民幣遂開始逐步升值並連帶地牽動亞洲其他國家幣值變化。為瞭解人民幣變動對亞洲四小龍國家幣值的外溢效果，本文利用動態條件相關係數模型，透過人民幣和亞洲四小龍貨幣的無本金交割遠期外匯分析相關係數。最後發現，人民幣和四小龍貨幣間存在不同程度的正相關，且此動態相關性自 2008 年起日與俱增。

本文研究保險人於匯率風險下之最適跨期投資組合。隨著資本市場全球化發展，從事國外投資受到匯率風險之影響加劇。本研究提出動態投資組合模型，針對壽險業之利變型商品，分析保險人於匯率風險之下之最適跨期投資組合。考慮資產集合包含本國現金、本國指數型股票基金、外國現金和外國指數型股票基金四項標的。本文研究方法主要以Cox & Huang(1989, 1991)平賭理論處理最適投資議題，將多期問題變為單期，求得保險人之最適投資組合。最後本文針對不同的匯率走勢與匯率風險波動度，利用電腦模擬，觀察不同風險趨避程度保險人之投資組合變化。 本文結果歸納如下： 1. 於風險市場價值、波動度和國內外無風險短期利率為定值下，保險人最適組合分別是擁有固定比例本國股票部位，外國股票部位則與匯率走勢呈負相關，而本國現金部位與外國現金部位呈現相反趨勢。發現匯率增量趨勢與外國現金帳戶、外國指數型股票基金和本國現金部位趨勢相同。 2. 匯率風險將影響保險人持有外國資產意願。若匯率風險波動度由0.1提高至0.3，則外國現金部位之最大值會從6.23下降到0.66。而外國股票持有部位於短期會增加，但隨著投資期限增加而逐漸遞減。同時短期增加之幅度小於外國現金減少之部分。整體而言，持有外國資產比例隨匯率風險波動度變大而遞減。 關鍵字：匯率風險、跨期投資組合、平賭理論、風險波動度、電腦模擬

本研究運用Vasecik、ARMA與VEC三種時間序列模型，以蒙地卡羅法，模擬未來五年台幣利率、美元利率與新台幣兌美元匯率的隨機漫步過程，並分析壽險公司的資產、負債與業主權益價值，在利率與匯率的隨機過程中所受到的影響。 藉由蒙地卡羅模擬之隨機漫步過程，本研究發現在利率模型方面，Vasicek利率模型因具有均數回歸的特性，較VEC模型擁有更穩定的隨機漫步過程；在匯率模型方面，VEC模型因同時考量長期影響與短期影響的效果，較ARMA模型擁有較穩定的漫步過程。 在負債面的模擬結果中，當利率下跌時，保單應提列準備金價值的成長速度較利率上升時快，此點反應壽險公司在低利率的環境下，將面臨較嚴峻的資本要求；同時，藉由歷史資料以Vasicek債券評價模型估計之利率期間結構，整體結構呈現負斜率與凹口向上的走勢，在此情形下，短期利率的值較長期利率的值高，保單應提列的準備金價值較原始估計時更高。 在長期的低利率環境中，上述現象反應於長期保單的價值變化尤為明顯。本研究建議在進行保單的精算訂價時，不應僅以預定利率做為保單全期的折現因子，而應將長期的利率風險納入考量。 同時，匯率的變化亦嚴重衝擊壽險公司的業主權益，在模擬結果中，當匯率落於風險值時，壽險公司配置於美元資產的減損將造成業主權益呈現虧損，此點亦反應當壽險公司將資產配置於海外時，必須謹慎地評估外匯避險的相關策略。 整體而言，在本研究中，將資產配置偏重台幣的投資策略擁有較穩定的業主權益價值，並在短期擁有較佳的風險轉換報酬能力；另一方面，將資產配置偏重美元的投資策略在長期擁有較佳的風險轉換報酬能力，然而，也因其擁有較高的風險值，壽險公司可能面臨較嚴重的損失。本研究建議壽險公司在進行海外資產配置時，應謹慎地將利率風險與匯率風險納入考量。 / This article uses Monte Carlo simulation method to forecast the random walk process of Taiwan interest rate, US interest rate, and Taiwan US dollar exchange rate between next five years. The simulation base on three time series model：Vasecik, ARMA and VEC. Through the random walk process, this article aims to analyze the influence in asset, liability and equity by the change of interest rate and exchange rate. In this paper, we find that the Vasicek interest rate model has a more stable stochastic process than the VEC model, which because of the effect by mean reversion. On the other hand, because the VEC exchange rate model takes both long-term and short-term impact in concern, it has a more robust stochastic process than the ARMA model. Through the simulation results of the liabilities, we find that when the interest rate fell, the reserve value of insurance policy will rise faster, which makes life insurance companies face more severe capital requirements in the low interest rate environment. Besides, we also find that the interest rate term structure in the Vasicek Bond Pricing Model displays negative slopes with concave upward, which means the value of short-term interest rate higher than the value of long-term interest rate. In this situation, the reserve value of insurance policy will become much higher than the value original priced. In the long-term low interest rate environment, the impact of interest rate risk has more effect in the long-term insurance policy. This paper suggests that when pricing the costs of insurance policy, we should not only use one interest rate as the full term discount factor. The better way is to discount with the interest rate term structure. Overall, in this paper, the asset allocation strategy, which focus on Taiwan commercial bonds, has both better performances in value at risk and better ability to covert risk into revenue in the short term. On the other hand, the asset allocation strategy, which focus on US commercial bonds, has better ability to covert risk into revenue in the long run. When conducting overseas asset allocation, we suggest that life insurance companies should carefully consider interest rate risk and exchange rate risk.

Abstract In time series analysis, we often find the trend of dynamic data changing with time. Using the traditional model fitting can't get a good explanation for dynamic data. Therefore, many scholars developed various methods for model construction. The major drawback with most of the methods is that personal viewpoint and experience in model selection are usually influenced in them. Therefore, this paper presents a new approach on genetic-based modeling for the nonlinear time series. The research is based on the concepts of evolution theory as well as natural selection. In order to find a leading model from the nonlinear time series, we make use of the evolution rule: survival of the fittest. Through the process of genetic evolution, the AIC (Akaike information criteria) is used as the adjust function, and the membership function of the best-fitted models are calculated as performance index of chromosome. Empirical example shows that the genetic model can give an efficient explanation in analyzing Taiwan exchange rates, especially when the structure change occurs.

本文主要是研究浮動匯率期間匯率波動對出口產業的影響。一般認為，匯率波動匯會使出口廠商的利潤風險增加，所以波動對於出口量的影響是為負的效果。不過，由於許多國外的研究的結果並不一定支持這種看法。本文針對台灣1984到1995年的資料進行實證研究，並且分別就不同出口產業對匯率波動的反應程度做討論，包括紡織類，塑膠化學類，電子類，機械類及基本金屬類五種產業，主要分為兩個架構分析： 　　（一）衡量匯率波動因子：對於匯率波動的衡量分成兩種方法：一種是以過去匯率變動的方式來衡量，另一種是以本期匯率預測的誤差來衡量，大部份的文獻都是採用前者。在此，為了將廠商事先避險的行為引入，所以採用後者的方法，將預測到的波動與未預測到的波動分離開來。 　　（二）匯率波動對各產業出口量的影響：將所有符合I(1)性質的變數用Johansen的方法做長期共整合關析的估計，再利用Granger Representation Theorem導出短期誤差修正模型，並將符合I(0)性質的波動因子引入模型當中，以便觀察匯率波動對出口量的影響。結果發現，各產業的出口量皆與匯率波動間存在明顯的負相關，其中以電子產業的影響最顯著，紡織類次之，基本金屬類影響最小，根據產品的特性分析可發現：當出口競爭愈激烈者，或是出口彈性愈大者，相對來講，會對匯率波動的反應較敏感。

我國過去以出口為導向的經貿政策，帶動了持續穩定的經濟成長並累積鉅額的外匯存底。近年來隨著經濟發展的日益蓬勃，國內的投資環境面臨了前所未有的衝擊；廠商為求企業之經營成長及競爭優勢，無不致力於降低生產成本，擴大市場規模，因此形成一股前往海外投資的熱潮。本文主要目的是利用「或有請求權法-購入選擇權(CallOption)」訂價理論分析國內出口廠商面對各項投資環境之不確定性因素衝擊時，如何決定「對外投資之最適時機」。因此，本文模型具有下列幾特點：（一）以個別廠商之觀點，探討對外投資之最適時機。（二）探討投資國及地主國生產成本相對變動時，對外投資最適時機之影響。（三）探討投資國及地主國外匯匯率變動時，對外投資最適時機之影響。（四）探討投資地主國享有對外優惠關稅待遇時，對本國廠商對外投資最適時機之影響。（五）探討廠商之研究發展成果與對外投資最適時機之影響。