The joint model of default and prepayment for a mortgage loan and its application in mortgage insurance

IF 2.2 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics Pub Date : 2026-03-01 Epub Date: 2026-01-29 DOI:10.1016/j.insmatheco.2026.103227

Lan Bu , Fang Wang , Jingping Yang

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引用次数: 0

Abstract

In a portfolio of loans, default and prepayment are two competing events, and only the time and type of the first event to occur can be observed. Modeling the competing risks is crucial for mortgage insurance. This paper focuses on modeling the joint distribution of the time to default and the time to prepayment by considering two components: subdistributions of the time to default and time to prepayment, and a copula to model their dependence structure, where the subdistributions are estimated from the portfolio data, and the copula is chosen by concentrating on some optimal criteria.

For this purpose, we discuss the compatibility of a copula with the given subdistributions, and provide a method for deriving the marginal distributions of default and prepayment from the subdistributions and a compatible copula. Moreover, two criteria are proposed for finding a copula compatible with the given subdistributions. For estimating the subdistributions, a bilinear model is proposed. The asymptotic properties of the model’s estimators are proved. Additionally, a simulation study demonstrates the consistency of the estimators by considering both large and small sample cases. Finally, an empirical study is performed to estimate the subdistributions with static and time-varying covariates, and to identify compatible copulas under the proposed criteria. The application of the proposed method is further highlighted for determining premiums of mortgage insurance.

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抵押贷款违约与提前还款联合模型及其在抵押贷款保险中的应用

在贷款组合中，违约和提前还款是两个相互竞争的事件，只能观察到第一个事件发生的时间和类型。对竞争风险进行建模对抵押贷款保险至关重要。本文通过考虑违约时间和提前支付时间的子分布，建立了违约时间和提前支付时间的联合分布模型，并建立了它们的依赖关系结构的联结关系模型，其中子分布由投资组合数据估计，并通过集中一些最优准则选择联结关系。为此，我们讨论了一种关联关系与给定子分布的相容性，并给出了一种从子分布和相容关联关系中推导违约和提前支付边际分布的方法。此外，还提出了两个准则来寻找与给定子分布相容的联结。为了估计子分布，提出了一种双线性模型。证明了模型估计量的渐近性。此外，仿真研究通过考虑大样本和小样本情况，证明了估计量的一致性。最后，对静态协变量和时变协变量的子分布进行了估计，并在所提出的准则下识别出相容的copuls。进一步强调了该方法在确定抵押保险保费方面的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Insurance Mathematics & Economics 管理科学-数学跨学科应用

CiteScore

3.40

自引率

15.80%

发文量

审稿时长

17.3 weeks

期刊介绍： Insurance: Mathematics and Economics publishes leading research spanning all fields of actuarial science research. It appears six times per year and is the largest journal in actuarial science research around the world. Insurance: Mathematics and Economics is an international academic journal that aims to strengthen the communication between individuals and groups who develop and apply research results in actuarial science. The journal feels a particular obligation to facilitate closer cooperation between those who conduct research in insurance mathematics and quantitative insurance economics, and practicing actuaries who are interested in the implementation of the results. To this purpose, Insurance: Mathematics and Economics publishes high-quality articles of broad international interest, concerned with either the theory of insurance mathematics and quantitative insurance economics or the inventive application of it, including empirical or experimental results. Articles that combine several of these aspects are particularly considered.