為使台灣公部門能利用確定提撥的概念及妥善運用投資資源，以期在減少政府負擔的情況下獲得足夠的退休所得，故本研究以所得替代率、金錢價值比及平均數-變異數比等指標來針對公務人員退撫基金附加節約儲蓄制度採行之可能與投資策略彼此運用之模擬結果加以分析，結果如下： 1. 各情境下以BH策略所得出之期末個人帳戶平均累積值表現最佳，然其具相當大的波動變異程度，投資人需承受相當大的風險。而TIPP策略之表現則與前述完全相反。 2. 若投資者採用BH策略或是採用CPPI與TIPP策略(CM策略)且欲追求較高的所得替代率，則建議採用Lifecycle(平衡型)的投資比例配置方式，加計DB制下之給付則平均可提供男(女)性約70.204%-75.204% (65.49%-70.49%)的所得替代率，而金錢價值比則為2.399(2.95)。 3. 無論投資者採用何種策略進行投資，若欲追求最小的可能變異風險，則建議採取平衡型的投資比例配置方式，加計確定給付制下之給付則平均可提供男(女)性約67.924%-72.924%(65.318%-70.318%)的所得替代率，金錢價值比則為2.6835。 本文模擬結果所得出之所得替代率平均維持於70%上下，代表若政府將可藉此制度減輕政府負擔外亦可使員工擁有一定水平的退休生活，故可採用。至於投資策略與配置方式如何取捨須依不同的投資者而定。 　 關鍵詞：公務人員退撫基金、確定提撥制、所得替代率、金錢價值比、Lifecycle / Abstract Because the improvement of medical technology and the structure of population is aging. It makes human worry about the living in the future. In order to enable the public servants of Taiwan to utilize the system of the Defined Contribution and to relief the pressure of fiscal, so we simulate in this article and analysis the results of simulation by using replacement rate, money’s worth ratio, and mean-variance ratio. The result is as follows: 1.When investor adopt the BH strategy in the process of investment, it will create the best replacement rate and money’s worth ratio under every situation, but it can be anticipated more uncertainty. Investors need to think thrice before they act. The TIPP strategy is opposite. 2.If investors adopt BH strategy or CPPI and TIPP strategy (CM strategy) and wanting to pursue the substituting rate of the higher income , the best selection is proposed adopting the Lifecycle (balanced) scenario, and it can offer replacement ratio about 70.204% - 75.204% (65.49% - 70.49% ) for the man (the woman ) under adding the DB system. Besides, the money’s worth rate is 2.399 (2.95). 3. If the investors want to pursue the least influence in the process of investment whatever investors adopt which strategies, the best scenario is the balanced type, and it can offer replacement ratio about 67.924%-72.924%(65.318%-70.318%) for the man (the woman) under adding the DB system. Besides, the money’s worth rate is 2.6835. The outcome of the simulation in this article is keep the replacement rate maintain about 70% equally, What is the best selection for investor that must be contingent upon different characteristics of investors. Keywords: public servants, Defined Contribution, Replacement rate, The money’s worth ratio, Lifecycle hypothesis.

本研究共包含三篇論文，首先修正von Hagen and Hepp(2000)所建立模型分析政府的財源轉移之風險分散與重分配動態效果。整體而言，補助與協助收入或統籌分配款所產生的所得與稅收風險分散或重分配效果相當有限，且各分區(北、中、南與全區)的結論差異甚大，顯示財源轉移發揮的效率不足。統籌分配款對於改善稅收的風險分散與重分配上，效果優於補助與協助收入。各縣市取得的補助與協助收入或統籌分配款高於長期所得與稅收風險分散與重分配所應對應的額度，造成資源浪費。就全區而言，前幾期稅收(所得)風險分散變化，可作為短期調整補助與協助收入(統籌分配款)的依據；統籌分配款與稅收的風險分散、補助與協助收入或統籌分配款與稅收重分配均存在雙向因果關係。 其次，在分析勞動者的休閒時間選擇時，本文修正跨期選擇模型，考慮勞動者持有投資組合與採取避險措施，並面對租稅問題下，以導出休閒時間方程式。實證上採用混合估計法針對12種樣本產業及兩種不同休閒時間衡量方式進行估計，結果顯示不同休閒時間衡量方式，影響估計結果甚鉅；金融市場的變化與波動攸關休閒時間變動：國內外利率、匯率與遠期匯率等與投資組合報酬相關的變數，在多數情況下顯著地影響休閒時間變動，且各變數對於休閒時間的影響程度，在工業中的次級產業大於服務業中的次產業。此外，採行周休二日制度確實改變制度採行前後的休閒時間，惟在三個工業次產業上則不明顯。 最後，修正Bo and Sterken (2002) 所建立的最適動態模型，分析公司價值不確定與租稅措施對海運廠商投資的影響，經由最大化公司價值導出影響台灣海運公司投資的三種不確定來源與避險措施，並進行實證估計。實證結果顯示，不確定的衡量方式攸關投資函數的估計結果，以指數加權移動平均標準差衡量不確定時，其估計結果優於以GARCH(1,1)衡量不確定，隱含廠商較在乎可預期波動對投資的影響。一般而言，廠商利率與原油價格的波動增加，均不利於公司投資，其中以原油價格不確定對於投資的影響最大，其效果約略與廠商利率相當。其次，影響海運公司投資最重要的三項因素均分別為BDI、負債與廠商利率，顯示價格與債務規模的重要性更甚於利率。此外，三種公司價值不確定來源對投資的影響，在多數個別公司之間並無顯著的差異，有助於採行總體財金政策以刺激投資。 / This dissertation contains three articles. First I revise the models set up by von Hagen and Hepp (2000) to analyze the dynamic effects of the Aid and Assistance and central government’s Tax Redistribution Fund on income (or tax) risk sharing and redistribution. For all the counties in Taiwan area the effects are tiny, but those are diverse among the counties in each Taiwan sub-area. The Aid and Assistance and central government’s Tax Redistribution Fund actually obtained by each county are larger than the amounts required to maintain long-term risk sharing and redistribution effects. These all imply that fiscal transfer is inefficiency. The effects of the central government’s Tax Redistribution Fund on risk sharing and redistribution are larger than those of Aid and Assistance. The central government can adjust the Aid and Assistance based on the change of earlier-period ax (income) risk sharing effect. Moreover, the existence of significant short-run interaction between the central government’s Tax Redistribution Fund and tax risk sharing, the Aid and Assistance and tax redistribution. Secondly, I revise intertemporal choice model by considering portfolio selection, hedging and taxation problems to derive economic agent’s leisure time equation. In empirical study, we focus on twelve sample industries and two different leisure time measurements, then adopt pooled estimation to estimate leisure time equation. Empirical results show that different measurement of leisure time influences estimation outcomes tremendously. Furthermore, the financial variables affecting portfolio return, including domestic and foreign interest rates, exchange rate and forward rate almost have remarkable effect on leisure time. Finally, the effect of each explanatory variable on leisure time is larger in industry than in service industry. Finally, I revise the optimal intertemporal model, constructed by Bo and Sterken (2002), by maximizing corporate value to derive three uncertainty sources and hedging influencing shipping-firm investment. Empirical evidences show that it is relevant for the estimation results to adopt which methods to measure the uncertainty. The outcomes derived from taking the Exponential Weighted Moving Average model to measure uncertainty are better than those from adopting the GARCH(1,1) model. Generally, as the volatilities in firm’s interest rate and crude oil price increase, firm investment decreases and the effect of crude oil price uncertainty on investment, the largest among the four effects, is nearly equal to that of firm interest rate on investment. Furthermore, BDI, debt and firm interest rate are the most important variables influencing firm investment. Finally, the effects of three uncertainty sources on investment are almost indifferent among the ten shipping-firms.

本文目的在於探討匯率不確定性對台灣出口波動之影響。本文應用Barkoulas et al.(2002)理論架構，利用台灣1989年至2007年的月資料。實證結果發現：美元、日圓兌新台幣的匯率波動對於台灣出口美、日兩國的數量並無明顯的影響。美元兌新台幣的匯率波動對於以美國為進口國的台灣出口波動則有正向的影響；日圓兌新台幣的匯率波動對於以日本為進口國的台灣出口波動卻沒有顯著影響。本文認為：造成美元匯率波動主要支配力量，來自於貨幣政策制定者掌握之資訊優勢差異；造成日圓匯率波動的來源則無主要支配力量的存在。造成此種結果的原因在於貨幣政策制定者長久以來所建立的政策可信度所致，削減了造成美元匯率波動的另外二股力量。因此，新台幣兌換美元匯率波動取決於貨幣政策制定者掌握經濟真實狀況的能力與其貨幣政策方向。 / This paper investigates into the effect of exchange rate uncertainty on Taiwan export volatility. Under the theoretical framework of Barkoulas et al.(2002) and the empirical monthly data of Taiwan exports from 1989 to 2007, it is summarized that the exchange rate volatility of NTD/USD and NTD/JPY had no effect on the Taiwan exporting volume toward U.S. or Japan. However, the exchange rate volatility of NTD/USD did have positive effect on the export volatility of Taiwan to U.S. while that of NTD/JPY had no significant effect on the export volatility of Taiwan to Japan.It is argued that the dominant source of NTD/USD exchange rate volatility resulted from the variance of monetary authorities’ information advantage. On the other hand, it exists no such a dominant source in NTD/JPY exchange rate volatility.

如何有效率管理或執行組織間交易活動，是學術界及實務界有興趣的議題。以成本觀點觀之，交易組織管理交易活動愈多，即代表付出的管理成本愈高。 本研究以交易買方角度，思考組織間交易過程中，我方管理交易活動複雜度。故本研究焦點設定在我方在決定與他方進行交易後，交易過程中的協調與管理活動。研究問題主要欲瞭解我方在決定交易對象後，執行該交易的管理成本為何；即瞭解影響我方管理交易付出活動多寡的因素為何。 為能確認研究議題相關之實務現象，本研究先進行個案研究，訪談六家電子產業公司、十二個交易個案。與理論對話後，整理出「我方交易管理複雜度」構面，並建構出本研究架構﹕考量交易特性、交易重要性及交易經驗與知覺他方投機行為對我方交易管理複雜度之影響。進一步地進行實證研究。 本研究透過問卷調查，共蒐集電子製造業產業170個有效交易樣本，研究假設經檢測後，本研究結果發現，在組織間交易過程中影響我方交易管理複雜度之因素包括：(1)交易任務流程的相互依賴程度愈高，因作業流程彼此銜接或為合作的資訊取得需要，我方管理重點將置於流程的協調，故我方會付出較多的管理行為來溝通協調交易的作業，包括對內整合與對外(即他方)溝通協調的管理活動。(2)交易任務不確定程度，包括交易品質的不確定與交易數量的不確定，我方將增加管理複雜度，例如進行監督、增加互動頻率或溝通來降低品質與交期的不穩定。(3)交易的重要程度高，表示該交易標的物取得對我方具有潛在優勢。當交易的作業重要性愈高時，我方在管理該交易時將增加管理行為取得或增加我方權力、或降低對他方的依賴，故我方交易管理複雜度將提高。(4)當我方知覺到他方有投機行為時，因交易任務流程相互依賴高的情況下，我方擔心資訊不對稱可能造成我方損失、或擔心我方須不平衡地多付出，我方除加強溝通協調取得更多作業資訊外，也須付出其他監督他方行為成本，形成我方整體交易管理愈趨複雜。 / Managing inter-organizational transactions efficiently is an important issue in practice and in research field. From cost perspective, when an organization manages transaction activities more, it pays the management cost more. This study takes the view of the buyer organization on transactions, and it considers the management complexity for inter-organizational transactions. It focuses on coordination and management for inter-organizational transactions after buyer organizations decided the transaction party. In other word, this research wants to explore what influence buyer organization to manage inter-organizational transaction on management cost. In order to explore the issues, this study adopted two study researches. At first, this study took 12 case studies form 6 companies to develop the construct of management complexity and build this research framework. Secondly, the study collected 170 samples of transaction in electronic industry by questionnaire investigation. The findings include below. (1) The higher the task-process interdependency is, the more management complexity buyer organizations pay for coordinating, communicating inter-organizational operational process or gathering more transaction information. (2) Task gets more uncertainty, including quality uncertainty and quantity uncertainty of transactions, then buyer organization will do more management complexity, e.g., monitoring transaction party and interacting frequently to each other. (3) As the transaction is important to buyer operations, buyer organization would do more management complexity in order to get more power in inter-organizational relationship or reduce dependency on transaction party. (4) If buyer organizations feel the transaction party opportunism, they would pay more attentions to safeguard. Especially, buyer organization will do something more to prevent getting loss from asymmetric information, when the task-process is getting more interdependent. Hence, the higher task-process interdependency trends to make buyer organizations pay more management complexity, when buyer organizations perceive higher opportunism

本研究主要分為三個部分：第一個部分探討壽險公司保單組合之最適資產配置；第二個部分探討確定提撥退休金制度下，員工所面臨的資產配置問題；第三個部分則為方法論的比較研究。此外，本文也探討長命風險(longevity risk)等相關議題。本文在Huang與Cairns (2006) 所提出的資產報酬模型下，推導出累積資產價值的期望值以及變異數，並利用套裝軟體的最佳化程式(optimization programming)獲得給定目標函數下的最適投資策略。 在保單組合資產配置之研究方面，我們分別針對保險公司繼續經營的商品以及即將停賣的商品提出合適的資產配置方式。常數資產配置方式(Constant rebalance rule)適合持續經營的商品，變動資產配置方式(Variable rebalance rule)則適合即將停賣的商品。在常數資產配置方式下，我們能夠得到投資組合的效率前緣線。此外，不管是何種資產配置方式，當保單組合的保單到期日較近時，保險公司必須增加其所持有的現金比例。 在確定提撥制下最適資產配置問題的研究方面，本文的結果符合一般退休基金經理人所採取的生命週期型態投資方式。本研究發現在Lee-Carter模型之下，考慮時間加權可以增加模型的預測能力。而在考慮長命風險下，員工必須採取更積極的投資策略。 本文決定資產配置之方法為預期模型(Anticipative model)，其在評價日時即決定未來的決策，不考慮新訊息對決策的影響。考慮新訊息會對決策產生影響的決定資產配置方法為適應模型(Adaptive model)。在第五章的研究裡，我們比較上述兩種決定資產配置方法之差異。研究結果發現，若以期望值與標準差為判斷標準，兩種決定資產配置方法並沒有絕對的優劣關係。而若在每個決策執行的時間點重新使用預期模型來決定新的資產配置策略，則其所對應的投資策略以及投資績效會與適應模型下的策略與投資績效接近。因此，在無法獲得適應模型投資策略封閉解的情況下，預期模型投資策略可以有效的近似適應模型投資策略。 / The purpose of this thesis is to investigate the asset allocation issue of the long-term investors. Our approach is to calculate theoretical formulae of the first two moments of the accumulated fund; we then adopt optimization programming to find a asset allocation strategy that fits the fund management target. Two kinds of investors are explored. The first one is an investment manager who manages a general portfolio of life insurance policies, and the second one is an employee who starts his career life in a DC pension plan. We also survey the longevity risk issue in this thesis. In the study of “optimal asset allocation for a general portfolio of life insurance policies”, two kinds of rebalancing methodologies are examined. For constant rebalance rule, which is applicable to a continuing business line, we find an efficient frontier in the mean-standard deviation plot that occurs with arbitrary policy portfolios. Also, the insurance company should hold more cash to reduce its illiquidity risk for portfolios in which policies will mature at earlier dates. In the study of “optimal asset allocation incorporating longevity risk in defined contribution pension plans”, we confirm the suitability of the lifestyle investment strategy. Investors in a DC pension plan should be more aggressive when he considers the longevity risk. Furthermore, we proposed a time adjustment technique to capture mortality predictions more precisely in this study. The approach of decision making of this thesis is referred to anticipative model, which does not consider the possible feedback from the future information. On the other hand, the approach of decision making that consider the possible feedback from the future information is referred to adaptive model. We further compare the two approached in the study “Comparative efficiency- anticipative model versus adaptive model”. The numerical results show that investors would not prefer the adaptive approach to the anticipative approach in the mean-variance criterion. Moreover, the downside risk is larger when the strategy is decided by adaptive approach. We also find that the strategy and its numerical distribution of anticipative approach can approximate to that of adapted approach if one re-assesses it at every decision date. Thus, the anticipative approach provides a first approximation on looking for the optimal investment strategy of adaptive model.

本研究設計了一些實驗來檢測學習完混沌資料的神經網路系統是否為混沌系統，驗證的方法是檢驗是否具有混沌資料的四個特性，這四個特性包括：有限性、非週期性、確定性、及對初始條件的敏感依賴。同時，更進一步地利用上述學習完的網路系統來預測所學習的混沌模型，這麼做的目的是想要了解：學習後的網路系統是一個混沌系統時，與學習後網路系統不是一個混沌系統時，其預測能力的比較。 此外，我們亦從理論上證明：學習完混沌資料後的神經網路系統無法重建其所學習的混沌模型。然而，有時網路系統卻能夠模擬成一個混沌系統；如果使用模擬成混沌系統的神經網路來預測具有混沌現象的資料，換句話說，也就可能是使用一個混沌系統去預測另一個混沌系統，根據混沌的特性 -- 對初始條件的敏感依賴，這樣的預測應該會造成相當大的誤差；不過，從本研究的實驗中發現，無論學習後的神經網路系統是否為一個混沌系統，對其預測能力並無顯著的影響。 本論文希望能給「用神經網路系統來預測具有混沌現象的金融市場或其他領域」一些貢獻與幫助。 / This paper uses some experimental designs to detect if the Neural Networks system after learning the chaotic data is a chaotic system. That is verified via testing four characteristics in chaotic data, inclusive of boundedness, determinism, aperiodicity and sensitive dependence on initial conditions. Further, this paper uses the result above to predict the learned chaotic model. The purpose is to probe into if the Neural Networks system after learning the chaotic data is a chaotic system and is used to predict, how good the short-term and the long-term predictions will be? And, compare with if the Neural Networks system after learning the chaotic data is not a chaotic system and is used to predict, how large the error will be? We present the Neural Network systems after learning the chaotic data never can rebuild the learned chaotic model. But, sometimes the Neural Network system would mimic as a chaotic system. So, if we take Neural Network system to predict something with chaotic phenomena, it is possible to use one chaotic system to predict another chaotic system. According to the property of sensitive dependence on initial conditions, it should make large errors. However, from the experiments we design, we find whether the Neural Network system after learning is a chaotic system or not, it has no influence on its predicting effect. This hint is applied to use ANN to predict in financial markets or other areas with chaotic phenomenon.

退休金計畫依給付方式的設計，可以分為兩大體系：確定給付退休金計畫與確定提撥退休金計畫。無論是公共退休金計畫或是企業退休金計畫，最初實行時多採用確定給付的方式來實施。但隨著經濟環境的變遷，部份的國家與企業雇主，已開始傾向確定提撥方式的採用。本論文有鑑於退休金的改革潮流，欲探討確定提撥退休金計畫的實施回顧與給付的精算分析。 本論文分為四個主要部分，分別為：(1)確定提撥計畫的理論架構回顧；(2)主要國家制度的分析；(3)精算模型的建立與精算假設的分析；與(4)精算假設的給定與給付水準的模擬分析。在主要國家制度的回顧上，公共退休金計畫方面以新加坡「中央公積金制」與智利「公共退休金私有化」為探討的對象；在企業退休金計畫方面則以美國為討論對象。實證分析部分，則是先建立確定提撥退休金精算模型，再撰寫模擬程式介面，並以我國1998年「勞工退休金條例」草案為模擬對象，給定精算假設進行模擬，最後分析精算假設與模擬給付間的關係。 以台灣「勞工退休金條例」草案為例進行分析，其實證部分分為兩部分，先前給定平準的預定利率假設，而其他薪資成長率、通貨膨脹率、提撥率、開始工作提撥年齡、退休年齡、退休後各年存活率則根據台灣目前的經濟、就業環境給定；模擬結果發現， 6％合併提撥率無法達到模擬所給定50％-60％的退休後給付所得替代率；若將合併提撥率提高至12％以上，25歲開始工作65歲退休者才能累積足以支應適足所得替代率50％-60％的給付。 第二個模擬部份為給定利率時間序列的情境假設，在此給定簡單的七種利率情境假設，其他精算假設則同樣根據台灣的經濟環境給定之。模擬結果發現，若合併提撥率為9％，基金提撥累積期間40年，給付所得替代率對利率的變動敏感性高，只有在累積期間利率穩定成長的情形下，才能累積足夠的退休金，因此，可以表示9％的合併提撥率在其他非樂觀的利率情境假設下，無法達到50％-60的給付所得替代率。 略 / Due to population aging, the countries that operated their Social Security System on pay-as-you-go financial method have begun to encounter the solvency risk due to the growing financial burden. Since the defined contribution (DC) scheme is considered as a fully funded financial system, it could be one of the solutions to avert the upcoming financial crisis. Hence our study is motivated to investigate the current development of the DC scheme and scrutinize its financial adequacy on providing the retirement benefits to its plan participants. First, the features of current public pension programs in the form of the DC plan are surveyed and their progress is reviewed in Chapter 2. Practical applications applying the DC scheme in private sector are also compared and studied in Chapter 3. Secondly, the actuarial models of the proposed DC scheme are built to investigate the adequacy of the retirement benefits in Chapter 4. Computer codes that can be used to simulate the income-replacement ratios by giving the actuarial assumptions are programmed. Based on this approach, the relationship between income-replacement ratios and the actuarial assumptions (i.e., the interest rate, the salary increase and the inflation rate) can be obtained. In Chapter 5, sensitivity analyses of the benefit adequacy through computer simulations incorporating possible scenarios are performed. The recent proposal of reforming Taiwan Employee Retirement Income Security Act (TERISA) is investigated. An explicit actuarial model closely following this proposal is built to study its impact on the retirement benefits. Finally the empirical results based on this study are summarized. Based on the scenarios under the current economic perspectives, we found the contribution rate at 6% can not attain the income-replacement ratio at 50%. Only over certain optimal interest rates, the retiree can receive the projected income-replacement ratio given the contribution rate at 9%. Based on the proposed draft in reforming the benefit scheme, the retirement benefits are not sufficient to achieve the income-replacement ratio at 50% unless the contribution rates increase to 12%.

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。

蒯因(W.V. quine)在語言哲學的發展上 , 可說是當代一大重鎮. 他對傳 統上在一般經驗論者中 , 對分析與綜合(analytic-synthetic)語句的區 分以及證實說(verificationism)提出嚴厲的批判,這可算是語言哲學中的 一大轉變 . 他的整體論(holism), 理論之不可由經驗完全限定 (unederdetermination of experiences) , 物理主義(physicalism) ,自然主義(naturalism) , 翻譯的不確定性(indeteriminacy of translation),指設的不可測度(inscrutability of references),存有學 的相對性(ontological relativity) 等理論 , 試圖以( 自然) 科學, 或說廣義物理理論作為我們對知識探求的基礎. 本文所要處理的問題是: 在翻譯的不確定性理論中, 蒯因所用的理論是什麼 ? 它是否有效而可以 成立 ? 其論證間是否各自獨立或有相互關係? In the development of philosophy of language, Quine is a very important philosopher. He criticized the traditional empiricism for the analytic-synthetic division and verificationism, this is an important milestone in the history of philosophy of language. He exhausts the whole theory, like holism, underdetermination of experiences ,physicalism, naturalized epsitemology, indetermincy of translation, and inscrutability of reference or ontological relativity, and so on. He tried to use sciences or broader physics to be the base of our researching for knowledge. The topic in this paper is about "indeterminacy of translation", we want to know Quine's arguments, the validity of these arguments, the relations between these arguments, and potential questions of this doctrine.

本文採用LIBOR市場利率模型評價確定提撥制退休金計畫所附之收益率保證，此保證收益率連結至隨機LIBOR市場利率，在相關的文獻上(特別在隨機利率方面)，尚未有相關的研究。本文同時考慮兩種保證型態：到期日保證與多期保證，運用平賭過程理論，在延伸之LIBOR市場利率模型(ELMM)下推導此兩種保證的理論公式解。相較於其他利率模型或HJM模型，採用ELMM所推得之評價公式更適合於實務運用。為供實務運用，文中並探討如何進行參數校準，亦進行蒙地卡羅模擬以驗證模型理論解的準確性。 / We derive the pricing formulas for the guarantees embedded in defined contribution (DC) pension plans with the guaranteed minimum rate of return set relative to a LIBOR interest rate. The guaranteed rate associated with a stochastic LIBOR interest rate has not yet been studied in the relevant literature, particularly in the presence of stochastic interest rates. An extended LIBOR market model (LMM) is employed to price the interest rate guarantees embedded in DC pension plans under maturity and multi-period guarantees. The pricing formulas derived under the extended LMM are more tractable and feasible for practice than those derived under the instantaneous short rate models or the HJM model. Calibration procedures are also discussed for practical implementation. Monte Carlo simulation is provided to evaluate the accuracy of the theoretical results.