Yes / We outline the valuation process for a No-Negative Equity Guarantee in an Equity Release Mortgage loan and for an Equity Release Mortgage that has such a guarantee. Illustrative valuations are provided based on the Black ’76 put pricing formula and mortality projections based on the M5, M6 and M7 mortality versions of the Cairns–Blake–Dowd (CBD) family of mortality models. Results indicate that the valuations of No-Negative Equity Guarantees are high relative to loan amounts and subject to considerable model risk but that the valuations of Equity Release Mortgage loans are robust to the choice of mortality model. Results have significant ramifications for industry practice and prudential regulation.

[pt] Entre 2006 e 2010, os preços de imóveis nos EUA caíram cerca de 30 por cento, fazendo com que o principal de um grande número de contratos de hipoteca ficasse abaixo do valor do imóvel. A teoria de default estratégico prediz que devedores nessa situação - chamada de negative equity value - deveriam entregar o imóvel e abandonar o contrato. Entretanto, a taxa de default em hipotecas com negative equity value, além de ser surpreendentemente baixa. Esta dissertação explica a baixa taxa de default no mercado americano de hipotecas a partir de preocupações dos credores em conseguir crédito imobiliário no futuro. O modelo mostra que tal preocupação é mais grave para devedores de baixa renda que se beneficiaram do crédito facilitado advindo da explosão de preços dos imóveis, mas que estão cientes de que tais facilidades provavelmente não estarão presentes no futuro. Os credores de baixa renda, portanto, têm mais incentivos a evitar default em hipotecas de negative equity value do que credores de mais alta renda, que antecipam facilidades em obter novo crédito imobiliário. Utilizando um painel de estados dos EUA para testar a existência deste efeito, mostramos que a inadimplência é mais sensível à queda no preço dos imóveis em áreas com maior renda per capita. / [en] Between 2006 and 2010, the price of houses in the United States fell by 30 percent, implying that a large number of mortgage contracts had negative equity value, that is, a debt outstanding higher than the house value. In these mortgage contracts, it pays for the borrowers to exchange their homes for the write-off of the debt. And yet, the delinquency rate among negative equity mortgages is surprisingly low. This paper argues that the fear of losing access to the credit markets explains why the delinquency rate remained relatively low in the U.S. after the Subprime crises. Our model shows that, with the end of the bubble in the housing market, low-income families are unlikely to qualify for the mortgage contracts they hold. Hence, fear of losing access to credit market lowers their incentive to walk away from their current mortgage contracts, even if they have negative equity value. Using a panel of US states to test the existence of this effect, we show that delinquency is more sensible to a decrease of house prices in areas with higher per capita income.

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.