承做反向房屋抵押貸款有許多的風險，包括有利率風險、房屋價值風險和死亡率風險，而當反向房屋抵押貸款的貸款餘額超過抵押房屋的價值時，則反向房屋抵押貸款的發行機構將會面臨了臨界風險。本文中的利率模型採用Black-Derman-Toy模型(BDT)來生成未來短期利率的機率分布；而房價模型方面則採用Cox-Ross-Rubinstein模型(CRR) ，死亡率模型為Lee-Carter模型。另外，本篇使用了三維度的四元樹模擬方法，觀察在短期利率模型與房屋價值模型相關的條件下，貸放機構將會面臨的預期損失。另外，對於承做反向房屋抵押貸款的貸放機構而言，最高可貸成數是由貸放機構未來預期損失的淨現值總合等於未來貸款保費的淨現值總合所求得。然而，當貸放機構未來所遭遇的實質損失大於預期損失時，貸放機構則將有未預期損失，因此為了移轉此非預期損失，我們設計了一個證券化的模型，希望藉由發行債券的方式，將此反向房屋抵押貸款發生在臨界點之後的臨界風險移轉給資本市場中的債券持有人。 / When the outstanding balance exceeds the housing value before the loan is settled, the insurer suffers an exposure to crossover risk induced by three risk factors: interest rates, house prices and mortality rates. Under the consideration of housing price risk, interest rate risk and longevity risk, we provide a three-dimensional lattice method which simultaneously captures the evolution of housing price and short-term interest rate to numerically calculate the fair valuation of reverse mortgages. For a mortgage reverse insurer, the maximum level of reverse mortgage insurance is determined by setting the present value of total expected claim losses equal to the present value of the premium charges. However, when the actual loss is higher than the expected loss, the insurer will incur an unexpected loss. To offset the potential loss, we also design a crossover bond, the payoff structure of which is related to the actual losses and expected losses, to transfer the unexpected loss into the bond investors. Therefore, through the crossover bonds, the reverse mortgage insurers can transfer the crossover risk into the bondholders.

壽險公司積極開發新商品以因應大量退休人口的需求，讓退休屋主得以所居住之房屋為抵押物，向金融機構貸款以獲得退休後之資金來源的反向房屋抵押貸款商品也應運而生。但這類的退休商品，除了讓壽險公司因人類平均壽命延長的現象而曝露在長壽風險的威脅下之外，其中所牽涉到之多樣的財務風險，也讓壽險公司在經營上面臨另外一個挑戰，但是反向房屋抵押貸款商品因其商品特性，似乎也可以提供壽險公司不同的風險分散的效果，有助於提升整體商品組合的避險效果。 本研究所提出之多因子免疫模型，可供壽險公司依照其所銷售之商品及所欲規避之風險，選擇一個最適的商品銷售數量，讓整個商品組合獲得最佳之避險效果。本研究透過多因子免疫模型進行數值分析，發現商品中加入反向房屋抵押貸款商品時，其避險效果明顯的優於未包含反向房屋抵押貸款之商品組合，顯見壽險公司發行反向房屋抵押貸款商品將有助於達到風險分散的效果，獲得更佳的避險成效。 關鍵字：長壽風險、財務風險、反向房屋抵押貸款、多因子免疫模型。 / Life insurance company try to meet the demand of the elder who has been retired by designing new products. The mortgage instruments to enable elderly homeowners to borrow by using the equity in their home as collateral, called “reverse mortgage”. With the launch this kind of product, life insurance company exposures in the threat of longevity and involves in others financial risks. However, the features of reverse mortgage may create the different effects of diversification for life insurance company to catch the better effects of hedging. We propose the Multi-Factors Immunization Approach to calculate the optimal product portfolio which attain the best hedging effects for life insurer by adjusting the number of units sold and recognizing the risks they want to hedge. We discover that the product portfolios which include reverse mortgage have the better hedging effects than these don’t include by numerical analysis. It is obviously that life insurer can acquire the effect of diversification and better hedging effects. Key words: Longevity risk, Financial risk, Reverse mortgage, Multi-factors immunization approach.

金融海嘯（financial tsunami）對全世界造成了相當大之衝擊，遭受最大損失者莫過於金融機構，其中房屋抵押貸款（mortgage）違約（default）產生之損失在銀行損失中占了一定的比例，本文認為深入研究影響違約之因素有其必要性。過去文獻於探討貸款違約時，主要可分為兩種學說，分別為權益學說（Equity Theory）與支付能力學說（Ability-to-Pay Theory），本文以台灣地區之實際房屋抵押貸款資料作為研究對象，以確認權益學說與支付能力學說於台灣房屋抵押貸款之適用程度。 本文採用二元羅吉特迴歸模型（Binomial Logit Regression Model, BLR）與比例危機模型（Proportional Hazards Model, PHM），並於權益學說之驗證中，考慮台灣房屋抵押貸款契約中常見之貸款追索權（right of recourse），以了解是否因借款人考慮追索權價值（value of recourse）而較不易違約。 實際結果發現，由於台灣長期房價趨勢皆為上漲之緣故，且台灣之貸款成數（Loan-to-value, LTV）較國外為低，導致處於負權益（Negative Equity）之抵押貸款筆數較少，然本研究發現，在修正了過去研究所使用之借款人權益變數後，其顯著性於BLR模型與PHM中皆較佳，而考量了追索權之價值後，考量追索權之修正後權益變數的表現更優於修正後之權益變數，顯示本研究於權益變數上之修正與考量追索權價值有助於模型改善違約預測之能力。 就權益學說與支付能力學說而言，由於兩種學說之相關變數皆有部分變數顯著，顯示兩種學說於台灣皆有其適用性，故於違約模型中需將權益學說與支付能力學說之相關變數皆列入考慮。 / Financial tsunami caused considerable impact in the world, and the financial institutions suffered huge losses in this crisis. Mortgage default losses accounted for a certain proportion in losses of financial institutes. It’s necessary to research the factors which influence the default decisions. In the past, the literatures divided the theory related to mortgage default into two parts, the Equity theory and the Ability-to-Pay theory. This article use the mortgage data in Taiwan to confirm which theory is more applicable in Taiwan. To understand if the borrowers would consider value of recourse when they make decision of default, this study adopts Binomial Logit Regression Model （BLR） and Proportional Hazards Model （PHM）, adding the right of recourse, which is common in the mortgage contract in Taiwan. The result shows that owing to the rising trend of Taiwan housing price and the lower loan-to-value （LTV） level than foreign countries, there are fewer mortgages in negative equity situation. However, we discover that after we modify equity variable, the modified equity variable is more significant than non-modified equity variable. Besides, if we consider the value of recourse, the modified equity variable with value of recourse performs best among three types of equity variable. The results above show that the modification of equity variable and the consideration of recourse can improve predicting ability of default model. And it shows the clause of recourse in Taiwan has certain influence on the decision of borrowers’ default behavior. Furthermore, the results of model illustrate the equity-related variables and ability-to-pay-related variables have certain explanation power on the behavior of default, which mean equity theory and ability-to-pay theory are applicable in Taiwan. We infer when carrying out the prediction of default, it’s necessary to take equity-related variables and ability-to-pay-related variables into consideration.

2007年美國爆發次級房貸違約潮造成了其經濟、房市和股市的不景氣，也波及到持有美國房貸證券化商品的各國，使其承受重大的損失，因此房屋抵押貸款違約的影響因素和金融資產證券化機制對貸款違約風險的影響又再度成為不動產與金融市場上之重要議題。而以往針對美國次貸危機的研究多指出道德風險是造成此次危機的原因之一，但是較缺乏實證研究的支持。 有鑑於此，本研究以我國的台北市和新北市的房屋抵押貸款市場作為研究對象，探討逆選擇和道德風險這兩個資訊不對稱的問題對貸款違約率的影響。研究結果顯示「貸款成數高、貸款利率高、搭配信貸和設定二胎的貸款比較容易違約」，證實逆選擇和道德風險問題確實存在於房屋抵押貸款市場，而且會增加貸款違約的機率。為了降低違約機率，從降低資訊不對稱的角度來看，本研究建議：一、建立全國房貸資料庫；二、將信貸的金額納入房貸的貸款成數中考慮，以降低款人的道德風險。 再者，本研究認為造成次貸危機的根本原因是不當政策導致的保證機制浮濫，以及高風險的房貸證券化商品的氾濫。為了避免我國發生類似次貸危機的事件，從減少資訊不對稱的角度切入，本研究建議我國的金融資產證券化機制應該：一、將道德風險內部化，消除創始機構自利的動機以減少道德風險；二、使用外部信用增強的方式，以確實發揮分散證券風險的作用。 / The 2007 subprime mortgage crisis has severely struck the stability of the worldwide financial markets. Some researches indicate that moral hazard problems are the main factors causing the crisis. However, few studies support asymmetry problems existing in a mortgage market by empirical evidences. First, using the mortgage samples from Taipei City and New Taipei City this study would like to understand if the mortgage market are information asymmetry problems, adverse selection and moral hazard, and conduct the empirical analysis for these factors’ impact on mortgage default. The results show that mortgage default is influenced significantly by the Loan-to-Value （LTV） ratio, contract interest rates, the existence of second liens and credit loans, and jobs. It shows that adverse selection and moral hazard actually exist in the mortgage market. According to the empirical results, secondly, this study proposes suggestions for mortgage lending and financial asset securitization to reduce adverse selection and moral hazard problems and enhance the regulation environment and market’s stability. It is expected that the results of this study will be applied to avoid the occurrence of similar crisis in Taiwan.

在台灣以服務型為導向的企業都致力於滿足客戶與顧客的需求，以求提升利潤，其中，帶給顧客滿足的重責大任幾乎都是由員工來執行；然而，近年來越來越常聽聞員工的福利與權益收到忽視甚至遭到擠壓。由此推論，一個不快樂的員工如何提供令顧客滿意的服務呢？因此，除了重視外部行銷以外，更是要強調內部行銷的落實。所謂內部行銷就是企業如何將公司及工作有效地行銷給員工，就如同將產品與服務行銷給外部顧客一般。 台灣的房仲產業競爭激烈，並強調顧客至上，而在這樣的情況下，公司仍否會重視對員工的照顧是本篇欲討論的重點。本研究以台灣本土房仲產業─信義房屋為研究對象，旨在探討其內部行銷作為與員工的心理擁有感表現。信義房屋目前為全台規模最大的房仲公司，創辦人周俊吉先生除了強調提供給顧客最優質的服務以外，也重視公司的永續經營與發展。此外，信義房屋是唯一一家上市的房仲公司並且連續被天下雜誌評選為天下企業公民。本研究採用半結構式深度訪談去發現公司的內部行銷作為，並進一步探究公司內部員工對公司本身以及信義房屋品牌的心理擁有感表現。 / Service-oriented companies mostly focus on carrying out external marketing which aims to provide best services to external customers. Traditionally speaking, this way seems to ensure higher revenue for companies. However, they are inclined to overlook the importance of employees who are reckoned as internal customers when applied to internal marketing. Nowadays, it is argued that focusing only on external customers would not ensure prosperity of the company. The application of internal marketing, clearly the opposite concept of external marketing, aims to sell the jobs and the company to its employees. More and more companies, especially service-oriented ones, acknowledge that the firm itself is supposed to bring satisfaction to its internal customers in accord with organizational objective before delivering satisfaction to external customers since most financial transactions occur between employees and customers. Specifically speaking, behaviors of employees have direct influences on customers and their ensuing consuming perceptions. In this regard, service firms should put much more emphasis on application of internal marketing. This study chooses Sinyi Realty as the research target in an attempt to explore its practices of internal marketing and ensuing performances of employee psychological ownership. Realty companies in Taiwan intensively compete with each other and thus put more emphasis on external customers. As for Sinyi Realty, a locally-developed and large-scale realty company, its founder and chairman Mr. Chou, Chun-Chi not only focuses on providing best services, but emphasizes sustainable management which is different from making fast money addressed by other realty companies. Besides, it is worth mentioning that it is the only listed realty company in Taiwan and has been awarded by Excellence in Corporate Social Responsibility many times. In this regard, this study adopts semi-structured in-depth interview to discover the real situation of internal marketing within the company. Most importantly, this study aims to explore performances of psychological ownership toward the company and the corporate brand among employees of Sinyi Realty. In fact, it follows two questions which are “how much do you feel the company is yours?” and “to what extent do you view the corporate brand as part of extended-self?” According to the case analysis, application of internal marketing found in Sinyi Realty exerts huge influences on employee psychological ownership, and also the impact of other critical factors cannot be underestimated. Based on the facts and discussion above, there are 8 derivative propositions in total that explicitly explain the relationships between internal marketing and psychological ownership; and other 3 propositions also manifest their close relations with psychological ownership for the organization and the corporate brand. Though these 11 derivative propositions are not discreetly examined by quantitative research method, they indeed present a general situation of Sinyi Realty and provide different research aspects for future study. At last, 4 managerial implications are proposed in expectation of enhancing the degree of psychological ownership among employees of Sinyi Realty by means of improved application of internal marketing.

在傳統銀行放款的觀念中認為，借款人主導了還款的來源，關於貸款風險的研究大多集中在借款人行為因素的探討，但是房屋貸款的風險，除了借款人本身的特質外，應該還需要不同角度的探討，尤其是在擔保品方面。銀行在辦理放款時，對擔保品價值的評估僅以當時的市場價值作直接的判斷，並依判斷結果來決定貸款的成數，這樣的決策並未考慮擔保品本身所處的區域條件及其未來的發展性，因而產生了風險判斷的偏誤。 本研究將透過不動產的供需價量的關係，嘗試找出影響房屋貸款擔保品風險的因子，並對房屋貸款的風險因子給予適當的權重及評分，再運用劃分等級的模型，將研究區域依房屋貸款風險的大小劃分風險等級。最後利用不同的角度或方法檢驗各種模型對區域風險分類之異同及功能，以建立模型提供銀行於承做房屋貸款或制定放款政策時，作為決定貸款成數(LTV)的參考依據，避免銀行貸款日後遭受擔保品價格下跌所產生的風險。 本研究以分析層級程序法(AHP)及分析網路程序法(ANP)設計不同的問卷，在取得各風險因子的權重後，對各項風險因子時間序列的數據進行分析，最終取得台北縣市各區域的風險等級。實證結果AHP及ANP皆通過一致性分析，AHP與未權重化ANP間不具顯著差異；權重化ANP與極限化ANP間不具顯著差異。AHP權重與ANP未權重化矩陣兩種模型在區域房屋貸款風險等級的區分標準上較為寬鬆。ANP權重化矩陣及ANP極限化矩陣對區域房屋貸款風險等級的劃分較為嚴格。這兩類不同等級劃分標準的模型提供金融業者在制定房屋貸款政策時可以有多樣的選擇。 / People with traditional concept of bank lending believe that borrowers dominate the sources of repayment. Researches regarding to the credit risk of loan mainly focus on the behaviors of borrowers. Nevertheless, the risk of mortgage loan should be deliberated with different points of view, especially the collateral, besides considering the characteristics of borrowers. During the process of loan, banks evaluate the collateral with directly determine according to the prevailing market value and decide the proportion of loan. The decision is not considered with the regional factors and the future development of the collateral. A bias of risk determination therefore exists during the process. The research tries to find the factors that influence the collateral risk of mortgage loan through supply, demand, price and quantity of real estate. Also, it allocates the weight and evaluation of every risk factor of mortgage loan. The research then distinguishes the investigated areas into different risk levels according to the mortgage loan risk by applying appropriate model. The research stands at various points of view and utilizes different methods to determine whether the classification of area risk is appropriate or not and offering a banks model to be the reference basis of determining the loan to value(LTV) when executing mortgage loan or drawing up loan policy. Banks can avoid the risk of collateral depreciation in the future. The research designed various questionnaires with Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP). After obtained the weights of different risk factors, an analysis was processed on time sequence data of every risk factor and results the risk level of every subarea of Taipei. The empirical results in consistency analysis by AHP and ANP are passed. The difference between AHP and un-weighted ANP is not significant. The difference between weighted ANP and limited ANP is also not significant. Both weighted AHP and un-weighted ANP matrix models are lenient on the classify criteria of area mortgage risk levels. In opposition, weighted ANP matrix models and ANP limited matrix are strict on the same criteria. The two models with different criteria offer financial corporations different choices when drawing up policies of mortgage loan

財產稅素來為政府重要財政收入，有關財產稅稅基計算為政府與民眾關心之重要議題。國際上財產稅稅基評估方式，依收益來源之不同，可分為由「租金收入」所得之年租金價值，或由「交易」所得之市場價值。我國財產稅稅基為土地申報地價與房屋評定現值，屬於以成本法評估之市場價值。 本研究經由稅基理論之文獻回顧，並針對臺北市觀光旅館與辦公大樓進行模擬分析與迴歸分析，研究結果發現，國際上財產稅稅基評估方式為市場價值或租金價值，應用於臺灣其實屬於「成本價值」與「收益價值」之爭。本研究認為，基於商業不動產經營獲利特性、交易型態與行政便利，並且符合量能課稅原則，商業不動產宜採用收益面之租金價值作為財產稅稅基；然而，現行制度僅反映不動產成本面，未反映不動產收益面。另外，若以租金價值作為稅基，需扣除無形資產之價值。 最後，若財產稅稅制轉變為以租金價值作為稅基，就旅館而言，於政策上可以鼓勵廠商興建大規模觀光旅館，並對經營初期業者有利，對於旅館產業發展有助益。就辦公大樓而言，於政策上可以鼓勵廠商興建大規模辦公大樓，可以促進開發者整合較大面積土地進行開發。 / Property tax is one of the important tax revenues of the government. People care about how to calculate property tax base. There are two values-based approaches that depends on different revenue sources one is “Annual Rental Value” which is based on rents, the other is “Market Value” which is based on sales. The Taiwanese property tax is based on market value and on cost approach. The study explores the tax base theories and use differential tax incidence and regression model to test the property tax bases of hotels and offices. According to the literature, there are two main ways to assess the property tax bases: Market Value Basis and Annual Rental Value Basis. However, it turns out to be the difference of Cost Value and Income Value in Taiwan. Due to the revenue-generating feature and transaction style of commercial properties, administrative convenience and the ability-to-pay principle, the study suggests that we should use annual rental value as the property tax base of commercial properties. Nevertheless, the Taiwanese property tax base only reflects the cost of properties, not the revenue-generating capacities of properties. On the other hand, the rent value includes the intangible assets such as famous brand names, the additional value which is not from the property should be excluded from the tax base. Nevertheless, if the rental value is substituted for the cost value as a tax base, there will be some possible situations as a reference for policy makers. For hotels, it will encourage firms to construct big scale hotels, and it will be beneficial for the initial operation of hotels. For offices, it will encourage firms to construct big scale offices and it will promote the developers to create more land area as well. Keywords: commercial property, property tax, house tax, cost value, rental value

【第一篇論文中文摘要】 集中度風險於結構式商品的量化與分析：以房屋抵押貸款證券為例 "Martin and Wilde (2002)與Gordy (2003)" 針對巴塞爾協定(Basel Accords)中金融機構之投資組合所內藴之集中度風險提出了相對應的微粒化調整(Granularity Adjustment)風險量化準則，然而該模型僅止於單因子架構下探究單一信用標的集中度風險之量化。本文將其架構延用至結構式商品中，允許債權群組內之信用標的具不同區域別，我們採用Hull and White(2010)之跨池違約相關性描述，並結合Pykhtin (2004)中延拓單因子聯繫模型至多因子之方式，進而求取債權群組之單一資產集中度(Name Concentration)與區域類別集中度(Sector Concentration)風險的量化。本文以房屋抵押貸款證券(Mortgage Backed Securities, MBSs)為例，於集中度風險的考量下，藉由檢視不同風險情境下分券之損失起賠點，重新評估房屋抵押貸款證券AAA投資級分券信用評級之合理性。研究結果顯示，AAA評等之分券高度曝險於系統性風險，且於高風險情境下，標的房貸之區域集中現象擴大了違約相關性對債權群組損失分配的影響，致使AAA分券之損失起賠點得以超過其實際擔保額度(subordination)範圍。 【第二篇論文中文摘要】 美國銀行放款多角化對其報酬與風險之影響：相關性與傳染的觀點 本文目的在於分析銀行放款的多角化行為對其報酬與風險之影響。研究發現納入銀行放款投資組合相關性之考量，亦即標的資產之相關性結構以及資產間因契約關係所隱含跨投資組合之傳染途徑，將降低多角化之成效。文中透過因子模型(factor model)建構資產之報酬，同時決定其相關性結構，其中將資產間殘差項相關性作為傳染指標，進一步分析投資組合內標的資產間的平均相關係數、傳染與多角化程度間的關聯性。我們以美國銀行作為研究樣本，分別以赫芬達-赫希曼指數估算投資組合權重分配之集中度、使用組合內標的產業股票報酬資訊來計算投資組合內相關程度，接著利用標的產業與投資組合外產業間的殘差相關性來捕捉產業傳染效果，將此三項指標作為衡量多角化指標，分析其在1987年至2014年間聯貸投資組合多角化情形並試圖分析放款多角化對銀行績效之影響。透過契約關係的界定進而探討顧客傳染如何影響銀行績效。 研究發現於市場處於平穩期間(tranquil period)，所有多角化指標銀行放款均呈現放款多角化程度越高越有助於提高銀行的報酬並降低其風險。然而於危機期間(turmoil period)，銀行應將放款權重集中於部分產業、建構相關性較低之組合或選擇較低之傳染效果之產業作為放款的對象，用以提高銀行績效。隱含在危機期間銀行應該選擇適度之多角化策略，若僅以赫芬達-赫希曼指數作為多角化之衡量將顯示危機期間越集中越有助於銀行的表現，此舉將造成解釋上的偏誤。說明於投資組合多角化的衡量上，不該忽略由相關性結構所引發之集中度風險。 / 【Essay I】 Quantification and Analysis of Concentration Risk in Structured Products: the Case of Mortgage Backed Securities Granularity adjustments, introduced by Martin and While (2002) and Gordy (2003), allow one to quantify the concentration exposures of credit portfolios due to imperfect diversification. However, they focus solely on name concentrations under an Asymptotic Single Risk Factor (ASRF) framework. In this study, by adapting the multi-pool correlation structure of Hull and White (2010) under the multi-factor setting of Pykhtin (2004), we derive quantitative measures of name and sector concentration that facilitate subsequent analysis of the risk profiles embedded in Mortgage Backed Securities (MBSs). Under different stress scenarios, we examine the impacts of concentration exposures on the internal credit enhancements, in particular, the AAA tranche attachment points. We show that, under severe market conditions, the presence of sector concentrations in the underlying mortgage pools can further amplify the effects of default correlation on the portfolio loss distributions. As a direct consequence, the predetermined subordination level determined by the assignment of tranche attachment points can be exceeded. 【Essay II】 How Loan Portfolio Diversification Affects U.S. Banks’ Return and Risk: Correlation and Contagion Perspectives. In this paper we investigate how loan portfolio diversification affects the banks’ return and risk. We argue that, the dependence structure of bank loan portfolios, namely, the correlation structure among loan assets and the presence of contagion channels due to contractual relationships across the border of portfolio, contributes to the costs of diversification. Under the factor model framework, we derive a theoretical model to depict the asset returns and their dependence structure. Based on data of US bank loans collected from 1987-2014, our empirical study employs HHI, intra-portfolio correlation, and contagion as proxies for diversification to examine how loan portfolio diversification affects the banks’ profitability and riskiness. In addition, contractual relationships are identified and we investigate how customer contagion affects the bank’s performance. We find that all diversification measures exhibit a positive effect on the performance of U.S. banks during tranquil periods. However, for turmoil periods, banks with loan portfolios of more concentrated weight distributions, lower intra-portfolio correlation, or lower consumer contagion effects would have improved returns and reduced risk. In other words, during crisis, banks should choose an appropriate concentration strategy rather than focus on selected industries as determined solely by the HHI.

房屋貸款保證保險制度可移轉部分違約風險予保險公司。然而，保險公司與金融機構在共同承擔風險之際，因房貸保證保險制度之施行，於提高貸款成數後，產生違約風險提高之矛盾現象；而估計保險之預期損失時，以目前尚無此制度下之違約數據估計損失額，將有錯估之可能。 本研究以二元邏吉斯特迴歸模型(Binary Logistic Regression Model)與存活分析(Survival Analysis)估計違約行為，並比較各模型間資料適合度及預測能力，進而單獨分析變數-貸款成數對違約率之邊際機率影響。以探討房貸保證保險施行後，因其對借款者信用增強而提高之貸款成數，所增加之違約風險。並評估金融機構因提高貸款成數後可能之違約風險變動，據以推估違約率數據，並根據房貸保證保險費率結構模型，計算可能之預期損失額，估算變動的保險費率。 實證結果發現，貸款成數與違約風險呈現顯著正相關，貸款成數增加，邊際影響呈遞增情形，違約率隨之遞增，而違約預期損失額亦同時上升。保險公司因預期損失額增加，為維持保費收入得以支付預期損失，其保險費率將明顯提升。故實施房屋貸款保證保險，因借款者信用增強而提高之貸款成數，將增加違約機率並對保險費率產生直接變動。 / Mortgage insurance system may transfer part of the default risk to insurance companies. However, the implementation of mortgage insurance system, on increasing loan to value ratio, the resulting increase default risk. And literatures estimate the expected loss without the default data, there will be misjudge. Our study constructs the binary logistic regression model and survival analysis to estimate the mortgage default behavior, and compare the data between the model fit and the predictive power. Analyzes the effect of loan to value ratio on the marginal probability of default rate. Furthermore, assess the financial institutions in the risk of default due to loan to value ratio changes. According to the estimated default rate data, we employ the mortgage insurance rate structural model to calculate the expected amount of loss and the changes in premium rates. Empirical results found loan to value ratio have a significant positive effect on borrowers’ default. Loan to value ratio increase, the marginal effect progressively increase, along with increasing default rates and expected default losses. Due to the ascendant expected loss, insurance companies increase premiums to cover the expected loss, the premium rate will be significantly improved. Therefore, the implementation of mortgage insurance, credit enhancement for the borrower to improve loan to value ratio, will increase the probability of default and insurance rates.