Valuation of Residential Mortgage-Backed Securities with Default Risk Using an Intensity-Based Approach

This paper develops a valuation model for fixed-rate mortgages, mortgage pools, and residential mortgage-backed securities (RMBS's) using an intensity-based approach. This model incorporates full prepayment, partial prepayment, and default in valuing a mortgage. Full prepayment is further classified into “refinancing” and “sale of a house” depending on the reason. The time of occurrence of each of these three types of prepayment and default is modeled as the first jump time of a Cox process. Under these conditions, the valuation formula for a mortgage as well as a partial differential equation (PDE) that the mortgage value satisfies is provided. As for implementation of the model, the short-term riskless interest rate and the house price are adopted as state variables. Each intensity process is specified in a manner that allows a jump in intensity depending on the state variables and the borrower's incentive for prepayment or default. Through such specifications, it is shown that our model has characteristics similar to some structural models in previous literature. As for the numerical method for valuation, we propose a simple backward induction technique on a tree instead of the commonly used Monte Carlo method. Additionally, the method for estimating the model is discussed, and the results of numerical simulations are reported.This paper represents the view of the author and does note necessarily the views of the Mitsubishi UFJ Securities Co., Ltd. or members of its staff.     

Analyses of Mortgage-Backed Securities Based on Unobservable Prepayment Cost Processes

We propose a prepayment model of mortgage based on a structural approach in order to analyze prepayment risk of mortgage-backed securities (MBS). We introduce a continuous process named prepayment cost process. Specifically, each mortgager's prepayment time is defined by the first time when her or his prepayment cost process falls below zero, but prepayment cost processes are supposed to be unobservable in the market. We also introduce a risk unique to each loan pool of mortgages, called a loan pool risk (LPR), and we regard LPR as a systematic risk other than interest rate. Using the model, we discuss the conditional distribution of prepayment times and a risk-neutral valuation of pass-through MBS. It is shown that each mortgager's conditional non-prepayment probability and the posterior distribution of LPR play quite important roles in our study.This research is partially supported by Grant-in-Aid for Young Scientists (B) No. 16710108 from the Ministry of Education, Culture, Sports, Science and Technology.     

Commercial Mortgage-Backed Securities: Prepayment and Default

One of the major developments in real estate finance during the 1990s was the emergence of a viable market for commercial mortgage backed securities. The growth in this market has spurred greater interest in empirical and theoretical research on commercial mortgage default and prepayment. We employ a competing risks model to examine the default and prepayment behavior of commercial loans underlying CMBS deals. We find that changes in the yield curve have a direct impact on the probability of mortgage termination. Furthermore, we do not find any statistical relationship between LTV and prepayment or default.     

Applied Nonparametric Regression Techniques: Estimating Prepayments on Fixed-Rate Mortgage-Backed Securities

We assess nonparametric kernel-density regression as a technique for estimating mortgage loan prepayments—one of the key components in pricing highly volatile mortgage-backed securities and their derivatives. The highly nonlinear and so-called irrational behavior of the prepayment function lends itself well to an estimator that is free of both functional and distributional assumptions. The technique is shown to exhibit superior out-of-sample predictive ability compared to both proportional-hazards and proprietary-practitioner models. Moreover, the best kernel model provides this improved predictive power utilizing a more parsimonious specification in terms of both data and covariates. We conclude that the technique may prove useful in other financial modeling applications, such as default modeling, and other derivative pricing problems where highly nonlinear relationships and optionality exist.     

Valuation of Mortgage Servicing Rights with Foreclosure Delay and Forbearance Allowed

We develop a bivariate binomial model to price Mortgage Servicing Rights (MSRs). Our model is an improvement over previous MSR pricing models by explicitly incorporating the realistic assumptions that there are additional costs involved in servicing delinquent loans. In addition to the Hilliard et al. mortgage-pricing tree, we extend additional sub-branches to model the borrower's decision of prepayment, cure, and foreclosure after a loan becomes delinquent. We then investigate how the value of the Mortgage Servicing Right varies with interest rate volatility, house price volatility, delinquency options, deficiency judgments, default penalties, forbearance periods, and speed of adjustments factors. JEL Classification: C15, G21     

Market Risk of Mortgage-Backed Securities with Consistent Measures

Due to the complex prepayment behavior, mortgage contracts and their derivatives are generally priced using Monte Carlo simulations. The typical approach used by the industry, which involves simulating interest rates under the risk-neutral measure and applying a physically measured prepayment function, is subject to the problem of internal inconsistency. This is the first paper that directly investigates the potential impact of this issue. Following the general equilibrium setting by Cox, Ingersoll and Ross, we incorporate the market risk price parameter to derive the physical interest rate process from an observed yield curve. This allows us to model mortgage values under the consistent physical measures of interest rates and prepayment functions. By analyzing a default-free Ginnie Mae MBS, we find that the mixed measures lead to slower prepayment rate estimates and overpriced mortgage securities by approximately 5%. Further, there can be substantial biases in the duration and convexity measures depending on market condition and the particular security of interest. The internal inconsistency also leads to biased predictions of both expected and stressed returns for different investment horizons. Depending on the particular security, the bias in expected and stressed returns can be either positive or negative. These biases in risk estimates can introduce misallocation of risk-based capital and/or failure in hedging the market risk of a mortgage-related portfolio.

个人住房抵押贷款违约风险跃迁概率研究

巴塞尔新资本协议提出针对个人住房抵押贷款可采用内部评级高级法评估其风险,在满足某些最低条件和披露要求的前提下,商业银行可根据自己对个人住房抵押贷款违约概率、违约损失率、违约风险暴露和期限等要素的估计值确定相应的资本要求。本文提出将风险跃迁概率引入到对个人住房抵押贷款提前还款-违约概率的定量估计中。借助逻辑斯特模型,本文将这一概念实际运用到对个人住房抵押贷款微观数据的分析当中,得到的实证研究结论包括借款人历史还款状态可以作为表征其未来还款状态的重要指标,贷龄与借款人还款状态的跃迁概率显著相关等。     

The valuation at origination of fixed-rate mortgages with default and prepayment

This paper develops a model to rationally price fixed-rate mortgages, using the arbitrage principles of option pricing theory. The paper incorporates amortization, prepayment and default in valuing the mortgage. Having completely specified the model, numerical procedures value the different features of the mortgage contract under a variety of economic conditions. The necessity of having both the interest rate and the house price as explanatory variables, due to the interaction of default and prepayment, is demonstrated. The numerical solutions presented center around mortgage pricing at origination. Thus, variations in the equilibrium contract rate are examined for differing economic conditions and changes in the contract. Finally, by presenting a complete model, the paper yields insights for the existence of common institutional practices.     

Bias in an Empirical Approach to Determining Bond and Mortgage Risk Premiums

Empirical studies of bond and commercial mortgage performance often quantify a required risk premium by examining the difference between the promised yield and the realized yield as adjusted for default occurrence. These studies omit the effects of various other sources of risk, however, including collateral asset market risk, interest rate risk, and possibly call risk. These omissions downwardly bias the empirical risk premium estimate on the debt. In this paper, we disentangle and quantify the sources of this bias by modeling secured coupon debt (the commercial mortgage) as used in the calculation of a realized investment return. We consider deterministic and stochastic interest rate economies with mortgage contracts that are either noncallable or subject to a temporary prepayment lockout period. Given realistic parameter values associated with the term structure, underlying asset dynamics, and debt contracting, we show that the magnitude of the bias can be significant.     

Valuation of the Firm's Liabilities When Equity Holders Are Also Creditors

Abstract:  This paper presents a tractable structural model whereby controlling equity holders are also among the creditors of the firm. As the firm approaches distress, equity holders can drain the assets of the firm and expropriate other creditors by repaying their credit before bankruptcy. The right of the bankruptcy court to revoke such repayment protects arm's length creditors, reduces the cost of borrowing and induces equity holders to anticipate repayment of their credit. Equity holders decide repayment neither too early nor too late, so as to reduce the risk of repayment revocation by the bankruptcy court. Similar conclusions apply to the preferential repayment of bank loans personally guaranteed by equity holders. The analysis also suggests that callable bearer bonds may be more valuable to equity holders than to other creditors.     

Competing Risks of Mortgage Termination: Who Refinances,Who Moves,and Who Defaults?

The Journal of Real Estate Finance and Economics - Why, when, and who terminates their mortgages? The primary reasons for mortgage termination are refinancing, selling of the property, and default....     

Housing-Price Cycles and Prepayment Rates of U.S. Mortgage Pools

Empirical mortgage prepayment models generally have trouble explaining differences in mortgage-prepayment speeds among pools with similar interest rates on the underlying mortgages. In this article, we model some of the sources of termination heterogeneity across mortgage pools, particularly the role of regional variations in housing prices in generating atypical prepayment speeds. Using a sample of Freddie Mac mortgage pools from 1991 to 1998, we compare two classes of empirical models: a rational option-pricing model using a backward-solving pricing algorithm and an empirical hazard model. In both empirical estimation strategies, we find evidence that differences in house-price dynamics across regions are an important source of between-pool heterogeneity. This finding is then shown to be robust to alternative ways of parameterizing pool heterogeneity in mortgage termination models.     

Valuation of a Credit Swap of the Basket Type

This article provides a simple model to value a credit swap ofthe basket type. Unlike the previous literature, we considerthe joint survival probability of occurrence times of creditevents in terms of stochastic intensity processes under the assumptionof conditional independence. Based on the joint survival probability,such a credit swap can be valued under the risk-neutral valuationframework. Assuming that the default intensity processes followthe extended Vasicek model with a correlation structure, an analyticexpression of the valuation formula is derived. Some numericalexample is given to demonstrate the usefulness of our model.     

An Early Assessment of Residential Mortgage Performance in China

The residential mortgage market becomes a financial engine for the booming residential housing development and sustained economic growth in China. Our study provides the first rigorous empirical analysis on the earlier performance of residential mortgage market in China based on a unique micro dataset of mortgage loan history collected from a major residential mortgage lender in China. We found that while the option theory fails to explain prepayment and default behavior in the residential mortgage market in China, other non-option theory related financial economic factors play major roles in determining the prepayment and default risks in China. We also found that borrower’s characteristics are significant in determining prepayment behavior, hence may be used as an effective tool for screening potential high risk borrowers in the loan origination process. Adopting a risk-based pricing in residential mortgage lending in China can improve the efficiency of the market, and enhance the credit availability to the most needed households, i.e., the younger households, blue-collar workers, lower income households, and help them become homeowners.     

基于会计信息的KMV模型实证研究

本文借助KMV模型框架,运用统计方法对大量的公司财务报表数据进行模型参数估计,计算得到了非上市公司的违约距离和经验EDF函数,实现了违约概率的模型估计。实证表明,我国公司在违约距离或违约数量上的真实概率分布均呈现显著的T分布和肥尾特性;违约距离具有较高的风险区分能力;由会计信息进行参数估计的模型导出的EDF具有较高的风险标识精度;进而表明基于会计报表数据的违约风险模型和基于资本市场数据的模型在实证上的有效性非常近似。     

A Finite Difference Approach to the Valuation of Path Dependent Life Insurance Liabilities

This paper sets up a model for the valuation of traditional participating life insurance policies. These claims are characterized by their explicit interest rate guarantees and by various embedded option elements, such as bonus and surrender options. Owing to the structure of these contracts, the theory of contingent claims pricing is a particularly well-suited framework for the analysis of their valuation.The eventual benefits (or pay-offs) from the contracts considered crucially depend on the history of returns on the insurance company's assets during the contract period. This path-dependence prohibits the derivation of closed-form valuation formulas but we demonstrate that the dimensionality of the problem can be reduced to allow for the development and implementation of a finite difference algorithm for fast and accurate numerical evaluation of the contracts. We also demonstrate how the fundamental financial model can be extended to allow for mortality risk and we provide a wide range of numerical pricing results.     

A Multicriteria Approach for Modeling Small Enterprise Credit Rating: Evidence from China

ABSTRACT

As the engine of China’s economy, small enterprises have been the central to the country’s economic development. However, given the characteristics of the small enterprises loan (i.e., short borrowing period, large volume, small amount and incomplete information), it is extremely challenging for financial institutions to assess their creditworthiness. Thus, it seriously delays and restricts the financing access for small enterprises. In an attempt to relieve the financing difficulty of small enterprises, this article makes use of 687 small wholesale and retail enterprises in a regional commercial bank in China, to establish a credit rating indicator system composed of 17 indicators by using both partial correlation analysis and probit regression. It then utilizes TOPSIS together with fuzzy C-means to score the credit ratings of our sample of small enterprises. With the dual test of default discrimination and ROC curve, the prediction accuracy of the established indicator system has reached 80.10% and 0.917, respectively, indicating the robustness and validity of our credit rating system.     

证券公司合规管理体系的现状、问题和对策

合规管理是企业全面风险管理的重要组成部分。近几年国内证券公司违法违规事件频发，系统性风险集中显现，与合规管理机制缺失密不可分。认真研究国内外金融业合规管理状况，加强国内证券公司外部合规法规体系建设，建立公司内部合规检查与监督机制，塑造合规文化，将有助于证券公司的规范经营和持续发展。     

基于情景的操作风险计量方法研究

《巴塞尔资本协议II》鼓励金融机构使用高级计量法计算监管资本,以此更加准确地反映金融机构的操作风险水平。其中,基于情景的计量法融合损失分布法、记分卡法的优势,能够更加前瞻性地计量操作风险资本。本文深入研究基于情景的计量法的流程、建模技术以及实际应用情况,提出应重视SBA在我国的应用和实践、建立完整的基于隋景的计量法体系、注重克服基于SBA可能存在的问题等建议,有利于国内银行根据实际情况考虑使用SBA计量操作风险监管资本和经济资本。     

地质成矿潜力价值评估方法

如何对矿业权进行有效评估,提高矿产资源利用率,关系到矿产资源的可持续发展。本文基于预期收益原则和地质要素评序法,从地质技术评估出发,提出了地质成矿潜力系数的概念,为合理确定矿业权的价值提出了地质潜力价值的评估方法;并利用该方法对具体案例进行了分析对比和评价,该案例的结果表明地质潜力价值评估方法具有较好的实用性,能够有效体现地质潜力价值。