不動產證券化可行性之研究 摘要 為解決傳統不動產投資困境，將不動產投資方式由固定的資產形式轉變為證券型態的概念，而有不動產證券化（Real Estate Securitization）的產生。國內主要的不動產證券化模式分為不動產投資信託（Real Estate Investment Trust）與不動產資產信託（Real Estate Asset Trust），這兩種模式未來市場供需面實際運作的可行性為何，將是不動產證券化制度成功與否的重要關鍵。 本研究先從需求面投資者的角度切入，透過問卷調查資料，運用Logit模型探討證券化可行性因素對於投資者購買不動產受益證券的影響。實證結果發現，一般投資者認為受益證券的市場流通性、分散風險的重要性愈高，以及預期報酬率愈高，其購買不動產受益證券的可能性愈高；在總體因素方面，對於未來證券市場情況愈樂觀，以及房地產市場情況愈樂觀，其購買受益證券的機率將愈高；法人投資者則認為分散風險的重要性愈高，以及該法人機構主要投資工具的種類愈多，其購買不動產受益證券的機率愈大。 以供給面不動產持有者財務上的可行性而言，其財務目標在追求自身的ROE極大化，因此不動產持有者將視各項風險來源對於投資報酬的影響，決定是否運用證券化投資方式。模擬分析結果發現，除了不動產持有者本身的財務結構限制與不動產經營能力之外，在個別考量委託成本風險與開發風險的情況下，其對於不動產持有者ROE的影響較小，但營運風險相較於其他風險來源，對於不動產持有者ROE的影響較大；綜合各項風險來源同時納入考量時，發現不動產持有者自有資金比例愈低，其運用證券化方式的ROE較高，但變動的幅度也較大。此一實證與模擬分析結果，對於未來國內不動產證券化實際運作，可提供政府、業者及一般投資大眾作為決策參考。 關鍵字：不動產證券化、不動產投資信託、不動產資產信託、Logit模型、蒙地卡羅模擬 / A Feasibility Study of Real Estate Securitization in Taiwai Abstract By transforming real assets into securities , real estate securitization is created to solve the liquidity problem of real estate investment. The real estate securitization system in Taiwan is divided into two types - Real Estate Investment Trust and Real Estate Asset Trust. Whether the real estate securitization system succeeds or not is based on the feasibility of the market operation in practice. On the demand side, this research uses Logit model to analyze the impact of the feasibility of the real estate securitization system on the investors’ behavior of buying beneficiary certificates by sampling from intuitional investors and individual investors. The empirical results show that the individual investors emphasize on liquidity, divergence, and expected return. In addition, the probability of buying real estate beneficiary certificates increases with the degree of their optimistic expectation on both the stock and the real estate markets. However, the institutional investors regard the divergence of portfolios and investment instruments as the main factors of their buying those certificates. On the supply side, given the financial objective of ROE maximum, the owners of the real estate will review all of impacts of risk on return of investment before their decision to take the way of securitization. In addition to the financial structure and the management ability of the owners, the results of Monte Carlo simulation on the effect of real estate securitization also reveal that: a. There is little influence on the ROE of the owners’ real assets while taking trust cost risk and land development cost risk into consideration. b. The influence of operation risk on ROE is more than that of other risks. c. Lower the proportion of capital, higher the ROE and bigger the variation of the ROE are. The results of empirical analysis can be a reference of decision making for Government, trust industry, and investors in the real estate security market operation. Keywords：Real Estate Securitization , Real Estate Investment Trust , Real Estate Asset Trust , Logit Model , Monte Carlo Simulation

影響海外可轉換公司債的因素有許多，包括股價、國內利率、國外利率、匯率，若將時間變數也加入計算，其變動因子高達5階，這種「高維度」的問題已非有限差分法或樹狀方法能處理；且海外可轉債常附有平均式條款、回顧式條款等「路徑相依」性質的選擇權，更是格狀結構數值法(Lattice)難以處理的問題。若使用蒙地卡羅模擬，雖然可以處理高維度及路徑相依的問題，但遇到美式契約時，則會有無法判斷轉換時點的問題，更遑論還必須處理的重設條款或界限型契約。 本論文研究海外可轉換公司債的評價，特點是可以處理其契約中各種可能的複雜條款，本文所使用的最小平方蒙地卡羅模擬，由Longstaff and Schwartz [2000]提出，對於美式契約、路徑相依及高維度問題皆可處理。本文並以Hull and White利率三元樹配適公司債利率符合市場利率期間結構。此外本研究加入海外可轉換公司債評價中最重要的信用風險因素，過去可轉債文獻理論價格大都高於實際市價，這是由於忽略了公司的信用風險溢酬，本文所使用的信用風險模型是由Lando [1998]所提出，特點是不以信用等級作為考量，探討公司特性與所屬產業，並考慮總體因素對違約機率的影響，從市場價格中估計違約密度參數，進而求得信用價差。 本研究對仁寶電腦在2002年所發的ECB做實證研究，比較LSM理論價格與實際市價之誤差，及對Takahashi[2001]所提出之歐式模型做比較，發現本文提出模型之評價結果相當不錯，誤差僅有0.83%；此外並對建華金控2002所發之ECB，探討各種複雜新奇條款對ECB價格的影響，發現市場上嚴重低估了重設條款所提高的價值，而實際市價卻十分接近僅含賣回條款的理論價格。

本論文的研究目的是在於分析在現階段的大環境下，即在利率低迷且經濟不景氣中，發行銀行如何針對投資者的需求，設計出可以吸引投資者前來投資的結構性新金融商品並從中獲取合理利潤。 本文以避險及保本兩大方向為出發點，選取了三個個案分析，分別是荷蘭銀行推出的『荷銀110%保證回報金價連動債券』、中國信託商業銀行推出的『中國信託商業銀行三個月期美元理財專案』、以及中國信託商業銀行推出的『中國信託商業銀行六個月期歐元理財專案』。 個案分析方式著重於在不同的利率下，計算出發行銀行發行商品之利潤、投資者之投資收益率、以及商品之避險部位分析，並針對商品之設計提出建議。

國內外對BOT實質選擇權之研究，大多集中於BOT主體本身所隱含之各種選擇權價值，鮮少論及BOT附屬事業之選擇權價值。惟因交通運輸BOT主體之自償率往往偏低，故須以保證最小運量或特許經營附屬事業等方式，來吸引潛在投資者。附屬事業對整個BOT計畫價值的影響頗大，如何針對其選擇權之價值加以分析為本研究的主要課題。個案將以台灣南北高速鐵路計畫為例，對其附屬事業之放棄選擇權加以探討。 本研究將主要探討下列課題，並提出研究結果： 一、有限差分法及蒙地卡羅模擬法計算選擇權價值，其間之差異？本 文利用有限差分法及蒙地卡羅模擬法來各別求算BOT 附屬事業的 放棄選擇權價值，一來了解 BOT 附屬事業的放棄選擇權價的大 小，二來比較有限差分法及蒙地卡羅模擬法兩者間的差異。 二、BOT附屬事業的放棄選擇權是否受主體事業的經營績效所影響？ 三、BOT附屬事業是否須考量履約保證金之設計？ 四、BOT主體決定經營或放棄時，是否會影響其附屬事業之放棄選擇 權價值？ 本研究係以蒙地卡羅模擬法及有限差分法單獨估計台灣南北高速鐵路附屬事業之放棄選擇權價值，並建立運輸主體與附屬事業間價值的關聯，再以蒙地卡羅模擬法作更精確的估算。另使用單因子變異數分析及Tukey's Multiple Comparison Method之統計方法，驗證BOT主體與其附屬事業選擇權間之相關性，期能有助於日後BOT計畫之參與者評估及決策使用。 / The study of the Real Option Analysis (ROA) thesis of BOT generally focus is on the principal parts of the project only, rarely is considered the option of ancillary business of BOT. Because the self-liquidation-ratio of the transportation of BOT is low, it needs the government financial support (minimum traffic guarantee or revenue enhancements) to attract the interest of intended investors. The influence of the ancillary business of BOT is huge, so how to evaluate the option is the big issue of thesis. The case focus on the Taiwan High Speed Rail BOT project, and will study the option value of it’s ancillary business. Thesis will discuss the following issues, and develop the result of study. 1.The calculation difference between Monte Carlo Simulation & Finite Difference Method to work out option value, Thesis will use the Monte Carlo Simulation & Finite Difference Method to work out the abandon option value of ancillary business of BOT. To get the abandon option value and compare the calculation difference between Monte Carol Simulation & Finite Difference Method. 2.Will the abandon option value of ancillary business of BOT be influenced by the principal parts of the project？ 3.Is there a need to consider the performance security deposit of ancillary business of BOT？ 4.Will the decision of BOT impact the abandon option value of ancillary business or not？ The thesis will use the Monte Carol Simulation & Finite Difference Method to calculate the abandon option value of ancillary business of Taiwan North-South High-Speed Railway Project (THR), and create the relation between the BOT & it’s ancillary business. The thesis will use the ANOVA & Tuley’s Multiple Comparison Method to validate the relationship, and hope it will let the participator to consider in the future.

歐式信用違約交換選擇權通常都以短天期較富流動信，造成這樣情形的原因很可能是因為長天期的信用違約交換選擇權必須承擔標的公司的倒閉風險。美式信用違約交換選擇權讓持有者可以在選擇權到期以前履約，這使得持有者可以只注意信用違約交換溢酬的變動，而不必擔心標的公司的倒閉風險。在這篇論文當中，我們結合最小平方法以及單期信用違約溢酬模型評價美式信用違約交換選擇權，其中單期信用違約溢酬模型是由布瑞格在2004年所發表的模型。本篇論文評價方法的最大優點在於此方法類似於利率理論的市場模型，因此我們可以利用類似的想法評價任何與信用違約交換合約相關的信用衍生性商品。 / The most liquid European CDS options are usually of short maturities. This may result from that options with longer maturity have to bear more default risk of the reference company. American CDS options allow the holders to exercise options before option matures so that they can focus on spread movements without worrying about default risk. In this paper, we price American CDS options with one-period CDS spread model presented by Brigo (2004). The primary advantage of this model is that it is similar to LIBOR market model in interest rate theory. Therefore, path-dependent CDS-related products can be easily priced with familiar ideas.

本文針對躉繳保費的附保證變額壽險進行評價，保單形式為生死合險，假設投保人可將期初的投資金額連結到兩種投資標的：股價指數及債券型基金，並以BGM模型描述利率的動態過程，然後分別計算不含解約權及含解約權的附保證變額壽險躉繳保費，進而求算出隱含在保單中的保證價值和解約權價值。針對含解約權的附保證變額壽險，以Longstaff and Schwartz(2001)提出的最小平方蒙地卡羅法處理解約的問題。最後，我們求算不同年齡下的男性保費，並且在投資比例、起始最低保證、最低保證給付成長率、針對解約的保證給付成長率和第一個允許的解約時點變動下，分別討論對於保證價值和解約權價值的影響。 結果顯示：(1)當起始最低保證給付等於期初投資金額時，投資在股票的比例越大，越能凸顯保證價值和解約權價值佔保費的比重。以30歲男性為例，保證價值佔不含解約權之附保證變額壽險的比例，由全部投資在債券型基金的0.03%，成長到全部投資在股票的13.86%；而解約權價值佔含解約權之附保證變額壽險的比例，由全部投資在債券型基金的0.05%，成長到全部投資在股票的9.12%。(2)投資比例、起始最低保證給付和最低保證給付成長率越大，保證價值越高。(3)起始最低保證給付和針對解約的保證給付成長率越大，解約權價值越大；而最低保證給付成長率和第一個允許的解約時點越大，解約權價值越小。(4)投資比例隨著最低保證給付不同對解約權價值有不同的影響。 關鍵字：附保證變額壽險、BGM利率模型、解約選擇權、最小平方蒙地卡羅法 / This study emphasizes on the pricing of variable life insurance with minimum guarantees. As an endowment policy in a single premium form, in this paper, it is assumed that the insured can distribute the initial investment amount into two underlying assets: the stock index fund and bond fund. Simulating the interest rate under a BGM model, computational procedures are performed for the single premium of the variable life insurance policy without surrender option and embedding a surrender option, and further, the guarantee value and surrender value embedded in the insurance policy. For the variable life insurance policy embedding a surrender option, the Least Square Monte-Carlo method proposed by Longstaff and Schwartz (2001) is applied to solve the surrender conditions. Finally, we calculate the premium for a male at different ages, and respectively analyze the variations of the guarantee value and surrender value under the influence of the investment portfolio, the initial minimum guaranteed amount, the growth rate of the minimum guarantee, the growth rate of the minimum guarantee for surrender and the first permitted surrender time. The results show that: (1) when the initial minimum guaranteed amount equals the initial investment amount, higher proportion invested in stock will result in larger percentage of the guarantee value and surrender value to total premium. Take a 30-year old male as an example: the percentage of guarantee value to the premium of variable life insurance with minimum guarantee and without a surrender option, which is 0.03% when the initial investment amount thoroughly goes to bond fund, rises up to 13.86% with the entire amount invested in stock index fund. Likewise, the percentage of surrender value to the premium of variable life insurance with minimum guarantee and surrender option is 0.05% with total amount invested in bond fund, while it is 9.12% with the entire amount invested in stock index fund. (2) The higher proportion invested in stock, the initial minimum guaranteed amount and the growth rate of minimum guaranteed amount, the larger guarantee value. (3) Larger initial minimum guaranteed amount and the growth rate of the minimum guaranteed amount for surrender would contribute to a higher surrender value. The higher growth rate of the minimum guaranteed amount and the first permitted surrender time, the lower surrender value. (4) The influence of the investment portfolio to surrender value depends on the initial minimum guaranteed amount. Key words: Variable life insurance with minimum guaranteed amount, BGM interest rate model, surrender option, least squares Monte Carlo approach.

本論文主要在估計門檻式自動迴歸模型之參數的信賴區間。由線性自動迴歸 模型衍生出來的非線性自動迴歸模型中，門檻式自動迴歸模型是其中一種經常會被應用到的模型。雖然，門檻式自動迴歸模型之參數的漸近理論已經發展了許多；但是，相較於大樣本理論，有限樣本下參數的性質討論則較少。對於有限樣本的研究，Woodroofe (1989) 提出一種近似法：非常弱近似法。 Woodroofe 和 Coad (1997) 則利用此方法去架構一適性化線性模型之參數的修正信賴區間。Weng 和 Woodroofe (2006) 則將此近似法應用於線性自動迴歸模型。這個方法的應用始於定義一近似樞紐量，接著利用此方法找出近似樞紐量的近似期望值及近似變異數，並對此近似樞紐量標準化，則標準化後的樞紐量將近似於標準常態分配，因此得以架構參數的修正信賴區間。而在線性自動迴歸模型下，利用非常弱展開所導出的近似期望值及近似變異數僅會與一階動差及二階動差的微分有關。因此，本論文的研究目的就是在樣本數為適當的情況下，將線性自動迴歸模型的結果運用於門檻式自動迴歸模型。由於大部分門檻式自動迴歸模型的動差並無明確之形式；因此，本研究採用蒙地卡羅法及插分法去近似其動差及微分。最後，以第一階門檻式自動迴歸模型去配適美國的國內生產總值資料。 / Threshold autoregressive (TAR) models are popular nonlinear extension of the linear autoregressive (AR) models. Though many have developed the asymptotic theory for parameter estimates in the TAR models, there have been less studies about the finite sample properties. Woodroofe (1989) and Woodroofe and Coad (1997) developed a very weak approximation and used it to construct corrected confidence sets for parameters in an adaptive linear model. This approximation was further developed by Woodroofe and Coad (1999) and Weng and Woodroofe (2006), who derived the corrected confidence sets for parameters in the AR(p) models and other adaptive models. This approach starts with an approximate pivot, and employs the very weak expansions to determine the mean and variance corrections of the pivot. Then, the renormalized pivot is used to form corrected confidence sets. The correction terms have simple forms, and for AR(p) models it involves only the first two moments of the process and the derivatives of these moments. However, for TAR models the analytic forms for moments are known only in some cases when the autoregression function has special structures. The goal of this research is to extend the very weak method to the TAR models to form corrected confidence sets when sample size is moderate. We propose using the difference quotient method and Monte Carlo simulations to approximate the derivatives. Some simulation studies are provided to assess the accuracy of the method. Then, we apply the approach to a real U.S. GDP data.

Fong與Vasicek（1997）提出風險分析應考慮敏感度分析、風險值及壓力測試，才能完整揭露投資組合的風險狀況。其中風險值的計算，不僅考慮二階風險，並且利用三階動差進行偏態修正。本文除了以變異數-共變異數法、歷史模擬法及蒙地卡羅模擬法此三種方法計算風險值，並利用Fong與Vasicek（1997）偏態修正法及Cornish-Fisher偏峰態修正法來做偏態及峰態的修正。而後再利用概似比檢驗法、回溯測試百分比法及Z檢定法作為驗證風險值模型的評比工具。我們建議在95%及99%的信賴水準下，求算風險值可利用Cornish-Fisher所提出的方法修正偏態及峰態。 / Fong and Vasicek (1997) mentioned that risk analysis should include sensitivity analysis, value at risk (VaR) and stress testing, in order to capture portfolio risk. The calculation of VaR should not only consider the second moment but should also adjust the skewness using the third moment. In this article, we determine VaR by employing three methods, the variance covariance, the historical simulation and the Monte Carlo simulation methods. In addition, we also adjust VaR for the skewness and kurtosis using the methods developed by Fong and Vasicek (1997) and Cornish-Fisher. Then, the likelihood ratio test, back testing and the Z-test are used to verify the VaR model. Our final test results suggest that calculating VaR should be adjusted for the skewness and the kurtosis as shown by the method proposed by Cornish Fisher in the 95% and 99% confidence intervals.

基於國內貸款市場的特性來看，國內金融機構所承作的不動產抵押貸款幾乎都是浮動利率抵押貸款，與美國以固定利率抵押貸款為主的貸款市場發展相當不同，未來台灣若欲發展不動產抵押貸款證券化，最先發展的商品應是符合國內抵押貸款屬性的調整利率傳遞證券，因此本文將針對調整利率傳遞證券做評價。同時，由於傳遞證券具有路徑相依的利率衍生性商品之性質，難以得到評價的封閉解，必須依賴數值方法來評價，評價方法不外乎採用利率樹或蒙地卡羅模擬法，本文將對此兩種評價方法做一深入的探討，同時有別於目前國內相關論文以Hull & White三元利率樹的評價方式，採用蒙地卡羅模擬法來評價，並進行敏感度分析，調整利率傳遞證券的評價結果如下： 1. 以台灣的貸款屬性來看，抵押貸款無每年利率上下限，雖有20％的最高利率上限但在目前低利率環境及低利率波動度的環境下，很難觸及此20％的最高利率上限，因此，期間利率上限價值很低，幾乎可視為一個純粹的浮動利率貸款。由於利率每年調整一次，現金流量則是按當時利率水準每月折現，故即使在貸款契約利率之利率加碼等於風險溢酬的情況下，傳遞證券的價格也不會等同於面值。 2. 利率波動度與調整利率傳遞證券價格之相關性不確定。 3. 調整利率傳遞證券價格與每年利率上限（annual cap）及期間利率上限（lifetime cap）有正相關。 4. 同時具有每年利率上限及下限的傳遞證券，價格會比只有每年利率上限的傳遞證券高。 5. 利率加碼越大，調整利率傳遞證券價格越高。 6. 提前清償速度與調整利率傳遞證券價格間的相關性，受到MBS折價或溢價的影響。

界限選擇權雖屬新奇選擇權的一種，但在國外卻已是交易頻繁的商品，而在國內則尚未有此一商品的交易發生。因此，為了能讓國內投資人與券商更了解此一商品，本研究便以界限選擇權為對象，針對其訂價與避險兩大主題進行研究，期能獲至有貢獻之結論。 在訂價方面，以二項評價模型對界限選擇權進行評價時，會產生鋸齒狀的收歛情況，對於精確評價界限選擇權造成極大的困擾。本研究對此問題提供一修正二項評價模型的方法，可以有效地消除評價時收歛不佳的現象。 在避險方面，本研究使用靜態避險法對其進行避險，並結合修正後之二項評價模型以建構在靜態避險法下所需之複製投資組合，此乃以往所未有之研究。在本文中所獲至之結果顯示，使用靜態避險法對界限選擇權進行避險所達成之避險效率實為在動態避險下所不能及；同時，隨著時間間隔的縮小，避險效率會隨之提高。此外，使用修正後之二項評價模型所建構之複製投資組合較以未修正之二項評價模型所建構之複製投資組合，在避險效率上會有較佳之表現。 第一章 緒論 1 第一節 研究背景 .1 第二節 研究動機與目的 1 第三節 研究架構與流程 2 第二章 界限選擇權之簡介及其應用 5 第一節 界限選擇權之簡介 5 第二節 界限選擇權之應用 7 第三章 文獻探討 14 第一節 選擇權訂價模式 14 第二節 界限選擇權之訂價 19 第三節 界限選擇權之避險 22 第四章 界限選擇權之訂價分析 23 第一節 二項評價模型之訂價法 23 第二節 對二項評價模型之修正 29 第三節 避險係數之分析 36 第五章 界限選擇權之避險分析 39 第一節 靜態避險法之介紹 39 第二節 避險效率之分析 43 第六章 結論與建議 62 第一節 結論 62 第二節 研究限制 63 第三節 後續研究建議 63 參考文獻 65 附錄：MATLAB程式 67 / Barrier option is one of those exotic options, yet it has been frequently traded in the foreign options markets. In Taiwan, this commodity is still new to most of us. Consequently, for a better understand and probably the issuance of this commodity, this research focuses on the pricing and hedging of barrier options, hoping that the research can obtain contributive conclusions. On pricing, when using CRR model as a pricing method for barrier options, there exists a situation which the convergence of the pricing is saw-toothed, contributing to the imprecise pricing results. This study provides a modification for the CRR model that can mitigate the saw-toothed convergence very effectively. On hedging, this study uses static hedge as a hedging measure, combining with the modified CRR model, which has very been studied before. The results of this study tell that, using static hedge can reach a very accurate hedging results, which is not attainable using dynamic hedge. Also, the more the time spacing shrinks, the more exact the hedge is. Finally, using modified CRR model as a basis producing replicating portfolio under static hedge can have a better performance in hedging than that of using unmodified CRR model.