Mortgage insurance (MI), is the insurance which a insurer guarantees that it will pay a certain portion of top tier mortgage loss to financial institution (insured) when the debtor defaults. Because the insurer shares the decreasing risk of collateral value, the bank is willing to lend homebuyer more money. The homebuyer can use low down payment (3%-10% in American) to buy a house so that he can shorten the waiting time of saving enough down payment. By this mechanism, the homebuyer, financial institution and house market all can benefit. Besides, mortgage insurance has the credit enhancement function in second mortgage market, and it helps the real estate securitization. The goal of this thesis is to introduce the mechanism of mortgage insurance in American and to analyze how it works in Taiwan. After estimating the need in Taiwan, I present some suggestions and I hope that mortgage insurance is available in Taiwan as soon as possible so that young people and earthquake 921 sufferers can make their owing house dream come true earlier.

none

國內首家專營住宅抵押貸款保證保險公司-美商聯合保證保險股份有限公司(United Guaranty, UG)，已獲得主管機關核准，於民國93年7月20日成立分公司，從事住宅抵押貸款保證保險業務。購屋者可因購買住宅抵押貸款保證保險，而使銀行願意提供高貸款成數的貸款服務，如此購屋者可降低自備款，而銀行的信用風險亦可得到保障。然此類保險業務對保險公司而言風險極大，若遇上經濟蕭條、失業率高漲時，損失率將快速提高，例如：美國於1930年代出現經濟大蕭條，許多產險公司因住宅抵押貸款保證保險業務理賠金額過多而紛紛倒閉，致使美國監理機關規定保險公司承作住宅抵押貸款保證保險業務需採單一險種（mono-line）的方式經營；再者，我國雖於民國54年奉准試辦「住宅抵押貸款償還保證保險」業務，其辦理目的在配合政府實行國宅政策，並協助個人在財力範圍內自置住宅，之後太平產險於民國86年推出「1090專案」，雖有一定的業務量卻也造成不少流弊，使保險公司承擔極大風險，故國內保險監理機關對住宅抵押貸款保證保險業務的態度趨於嚴格。 本文主要在探討住宅抵押貸款保證保險於我國保險法上之適用，及其於實務上運作已發生或可能發生的問題。保險法雖於民國81年增訂保證保險專節，使保證保險有法源依據，但由於規定過於簡單，故我國保險學界與實務界對其定位有相當分歧的看法，住宅抵押貸款保證保險屬保證保險的一種，故藉由探討保證保險的法律性質與定位，以釐清住宅抵押貸款保證保險可能產生法律適用上的疑義。而對於住宅抵押貸款保證保險的實務運作，則是藉由介紹國外住宅抵押貸款保證保險發展與趨勢，針對國內當前金融環境與風險管理的角度，試著提出對國內住宅抵押貸款保證保險發展方向與監理方向上之建議。

住宅抵押貸款保險(Mortgage Insurance)為管理違約風險的重要工具，在2008年次級房貸風暴後更加受到金融機構的關注。為了能更準確且更有效率的預測房價及合理評價住宅抵押貸款保險，本文延續Christoffersen, Heston and Jacobs (2006)對股票報酬率的研究，提出新的GARCH模型，利用Inverse Gaussian分配取代常態分配來捕捉房價序列中存在的自我相關以及典型現象(stylized facts)，並且同時考慮房價市場中所隱含的價格跳躍現象。本文將新模型命名為IG-GARJI模型，以便和傳統GARCH模型作區分。由於傳統的GARCH模型在計算保險價格時，通常不存在封閉解，必須藉由模擬的方法來計算價格，會增加預測的誤差，本文提供IG-GARJI模型半封閉解以增進預測效率與準確度，並利用Bühlmann et al. (1996)提出的Esscher transform方法找出其風險中立機率測度，而後運用Heston and Nandi (2000)提出之遞迴方法，找出適合的住宅抵押貸款保險評價模型。實證結果顯示，在新建房屋市場中，使用Inverse Gaussian分配會比常態分配的表現要好；對於非新建房屋，不同模型間沒有顯著的差異。另外，本文亦引用Bardhan, Karapandža, and Urošević (2006)的觀點，利用不同評價模型來比較若房屋所有權無法及時轉換時，對住宅抵押貸款保險價格帶來的影響，為住宅抵押貸款保險提供更準確的評價方法。 / Mortgage insurance products represent an attractive alternative for managing default risk. After the subprime crisis in 2008, more and more financial institutions have paid highly attention on the credit risk and default risk in mortgage market. For the purpose of giving a more accurate and more efficient model in forecasting the house price and evaluate mortgage insurance contracts properly, we follow Christoffersen, Heston and Jacobs (2006) approach to propose a new GARCH model with Inverse Gaussian innovation instead of normal distribution which is capable of capturing the auto-correlated characteristic as well as the stylized facts revealed in house price series. In addition, we consider the jump risk within the model, which is widely discussed in the house market. In order to separate our new model from traditional GARCH model, we named our model IG-GARJI model. Generally, traditional GARCH model do not exist an analytical solution, it may increase the prediction error with respect to the simulation procedure for evaluating mortgage insurance. We propose a semi-analytical solution of our model to enhance the efficiency and accuracy. Furthermore, our approach is implemented the Esscher transform introduced by Bühlmann et al. (1996) to identify a martingale measure. Then use the recursive procedure proposed by Heston and Nandi (2000) to evaluate the mortgage insurance contract. The empirical results indicate that the model with Inverse Gaussian distribution gives better performance than the model with normal distribution in newly-built house market and we could not find any significant difference between each model in previously occupied house market. Moreover, we follow Bardhan, Karapandža, and Urošević (2006) approach to investigate the impact on the mortgage insurance premium due to the legal efficiency. Our model gives another alternative to value the mortgage contracts.

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.

Many analysts believe that problems in the U.S. housing market initiated the 2008–2010 global financial crisis. In this regard, the subprime mortgage crisis (SMC) shook the foundations of the financial industry by causing the failure of many iconic Wall Street investment banks and prominent depository institutions. This crisis stymied credit extension to households and businesses thus creating credit crunches and, ultimately, a global recession. This thesis specifically discusses the SMC and its components, causes, consequences and cures in relation to subprime mortgages, securitization, as well as data. In particular, the SMC has highlighted the fact that risk, credit ratings, profit and valuation as well as capital regulation are important banking considerations. With regard to risk, the thesis discusses credit (including counterparty), market (including interest rate, basis, prepayment, liquidity and price), tranching (including maturity mismatch and synthetic), operational (including house appraisal, valuation and compensation) and systemic (including maturity transformation) risks. The thesis introduces the IDIOM hypothesis that postulates that the SMC was largely caused by the intricacy and design of subprime agents, mortgage origination and securitization that led to information problems (loss, asymmetry and contagion), valuation opaqueness and ineffective risk mitigation. It also contains appropriate examples, discussions, timelines as well as appendices about the main results on the aforementioned topics. Numerous references point to the material not covered in the thesis, and indicate some avenues for further research. In the thesis, the primary subprime agents that we consider are house appraisers (HAs), mortgage brokers (MBs), mortgagors (MRs), servicers (SRs), SOR mortgage insurers (SOMIs), trustees, underwriters, credit rating agencies (CRAs), credit enhancement providers (CEPs) and monoline insurers (MLIs). Furthermore, the banks that we study are subprime interbank lenders (SILs), subprime originators (SORs), subprime dealer banks (SDBs) and their special purpose vehicles (SPVs) such as Wall Street investment banks and their special structures as well as subprime investing banks (SIBs). The main components of the SMC are MRs, the housing market, SDBs/hedge funds/money market funds/SIBs, the economy as well as the government (G) and central banks. Here, G either plays a regulatory or policymaking role. Most of the aforementioned agents and banks are assumed to be risk neutral with SOR being the exception since it can be risk (and regret) averse on occasion. The main aspects of the SMC - subprime mortgages, securitization, as well as data - that we cover in this thesis and the chapters in which they are found are outlined below. In Chapter 2, we discuss the dynamics of subprime SORs' risk and profit as well as their valuation under mortgage origination. In particular, we model subprime mortgages that are able to fully amortize, voluntarily prepay or default and construct a discrete–time model for SOR risk and profit incorporating costs of funds and mortgage insurance as well as mortgage losses. In addition, we show how high loan–to–value ratios due to declining housing prices curtailed the refinancing of subprime mortgages, while low ratios imply favorable house equity for subprime MRs. Chapter 3 investigates the securitization of subprime mortgages into structured mortgage products such as subprime residential mortgage–backed securities (RMBSs) and collateralized debt obligations (CDOs). In this regard, our discussions focus on information, risk and valuation as well as the role of capital under RMBSs and RMBS CDOs. Our research supports the view that incentives to monitor mortgages has been all but removed when changing from a traditional mortgage model to a subprime mortgage model. In the latter context, we provide formulas for IB's profit and valuation under RMBSs and RMBS CDOs. This is illustrated via several examples. Chapter 3 also explores the relationship between mortgage securitization and capital under Basel regulation and the SMC. This involves studying bank credit and capital under the Basel II paradigm where risk–weights vary. Further issues dealt with are the quantity and pricing of RMBSs, RMBS CDOs as well as capital under Basel regulation. Furthermore, we investigate subprime RMBSs and their rates with slack and holding constraints. Also, we examine the effect of SMC–induced credit rating shocks in future periods on subprime RMBSs and RMBS payout rates. A key problem is whether Basel capital regulation exacerbated the SMC. Very importantly, the thesis answers this question in the affirmative. Chapter 4 explores issues related to subprime data. In particular, we present mortgage and securitization level data and forge connections with the results presented in Chapters 2 and 3. The work presented in this thesis is based on 2 peer–reviewed chapters in books (see [99] and [104]), 2 peer–reviewed international journal articles (see [48] and [101]), and 2 peer–reviewed conference proceeding papers (see [102] and [103]). / Thesis (Ph.D. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2011.

Many analysts believe that problems in the U.S. housing market initiated the 2008–2010 global financial crisis. In this regard, the subprime mortgage crisis (SMC) shook the foundations of the financial industry by causing the failure of many iconic Wall Street investment banks and prominent depository institutions. This crisis stymied credit extension to households and businesses thus creating credit crunches and, ultimately, a global recession. This thesis specifically discusses the SMC and its components, causes, consequences and cures in relation to subprime mortgages, securitization, as well as data. In particular, the SMC has highlighted the fact that risk, credit ratings, profit and valuation as well as capital regulation are important banking considerations. With regard to risk, the thesis discusses credit (including counterparty), market (including interest rate, basis, prepayment, liquidity and price), tranching (including maturity mismatch and synthetic), operational (including house appraisal, valuation and compensation) and systemic (including maturity transformation) risks. The thesis introduces the IDIOM hypothesis that postulates that the SMC was largely caused by the intricacy and design of subprime agents, mortgage origination and securitization that led to information problems (loss, asymmetry and contagion), valuation opaqueness and ineffective risk mitigation. It also contains appropriate examples, discussions, timelines as well as appendices about the main results on the aforementioned topics. Numerous references point to the material not covered in the thesis, and indicate some avenues for further research. In the thesis, the primary subprime agents that we consider are house appraisers (HAs), mortgage brokers (MBs), mortgagors (MRs), servicers (SRs), SOR mortgage insurers (SOMIs), trustees, underwriters, credit rating agencies (CRAs), credit enhancement providers (CEPs) and monoline insurers (MLIs). Furthermore, the banks that we study are subprime interbank lenders (SILs), subprime originators (SORs), subprime dealer banks (SDBs) and their special purpose vehicles (SPVs) such as Wall Street investment banks and their special structures as well as subprime investing banks (SIBs). The main components of the SMC are MRs, the housing market, SDBs/hedge funds/money market funds/SIBs, the economy as well as the government (G) and central banks. Here, G either plays a regulatory or policymaking role. Most of the aforementioned agents and banks are assumed to be risk neutral with SOR being the exception since it can be risk (and regret) averse on occasion. The main aspects of the SMC - subprime mortgages, securitization, as well as data - that we cover in this thesis and the chapters in which they are found are outlined below. In Chapter 2, we discuss the dynamics of subprime SORs' risk and profit as well as their valuation under mortgage origination. In particular, we model subprime mortgages that are able to fully amortize, voluntarily prepay or default and construct a discrete–time model for SOR risk and profit incorporating costs of funds and mortgage insurance as well as mortgage losses. In addition, we show how high loan–to–value ratios due to declining housing prices curtailed the refinancing of subprime mortgages, while low ratios imply favorable house equity for subprime MRs. Chapter 3 investigates the securitization of subprime mortgages into structured mortgage products such as subprime residential mortgage–backed securities (RMBSs) and collateralized debt obligations (CDOs). In this regard, our discussions focus on information, risk and valuation as well as the role of capital under RMBSs and RMBS CDOs. Our research supports the view that incentives to monitor mortgages has been all but removed when changing from a traditional mortgage model to a subprime mortgage model. In the latter context, we provide formulas for IB's profit and valuation under RMBSs and RMBS CDOs. This is illustrated via several examples. Chapter 3 also explores the relationship between mortgage securitization and capital under Basel regulation and the SMC. This involves studying bank credit and capital under the Basel II paradigm where risk–weights vary. Further issues dealt with are the quantity and pricing of RMBSs, RMBS CDOs as well as capital under Basel regulation. Furthermore, we investigate subprime RMBSs and their rates with slack and holding constraints. Also, we examine the effect of SMC–induced credit rating shocks in future periods on subprime RMBSs and RMBS payout rates. A key problem is whether Basel capital regulation exacerbated the SMC. Very importantly, the thesis answers this question in the affirmative. Chapter 4 explores issues related to subprime data. In particular, we present mortgage and securitization level data and forge connections with the results presented in Chapters 2 and 3. The work presented in this thesis is based on 2 peer–reviewed chapters in books (see [99] and [104]), 2 peer–reviewed international journal articles (see [48] and [101]), and 2 peer–reviewed conference proceeding papers (see [102] and [103]). / Thesis (Ph.D. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2011.