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.     

Valuation of Mortgage-Backed Securities Based upon a Structural Approach

This paper studies the valuation of mortgage-backed securities (MBS) based upon a structural approach of several risks involving the prepayment and/or default behavior of mortgagors. For the Kariya and Kobayashi (1999) model using a time-consuming Monte-Carlosimulation, we provide an alternative semi-analytic valuation methodology closely related to solving the (Volterra type) integral equation with respectto the first hitting time density for a curved/flat boundary; consequently that enables us to calculate the MBS price faster and more precisely. Next, to capture the path-dependent prepayment behavior of the interest ratemovements we give some prepayment models based upon a two-dimensional Markov process of the interest rate and its long-run average rate. Third, we study the simultaneous assessment issue of prepayment and defaultrisks, encountered in practice.Finally we discuss the calculation of the joint probability density ofmultiple first hitting times.     

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 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     

Anatomy of an ARM: The Interest-Rate Risk of Adjustable-Rate Mortgages

This article analyzes the dynamics of the commonly used indices for adjustable rate mortgages and systematically compares the effects of their time-series properties on the interest-rate sensitivity of adjustable-rate mortgages. Our ARM valuation methodology allows us simultaneously to capture the effects of index dynamics, discrete coupon adjustment, mortgage prepayment, and both lifetime and periodic caps and floors. We can, moreover, either calculate an optimal prepayment strategy for mortgage holders or use an empirical prepayment function. We find that the different dynamics of the major ARM indices lead to significant variation in the interest-rate sensitivities of loans based on different indices. We also find that changing assumptions about contract features, such as loan caps and coupon reset frequency, has a significant, and in some cases unexpected, impact on our results.     

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。     

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.     

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.

The Hazard Rates of First and Second Defaults

This article examines hazards of repeated mortgage default, conditional on reinstating out of an initial default episode. Results indicate that subsequent default risk for reinstated borrowers is significantly greater than the risk of first default, especially during the first two years after a default episode. In addition, economic factors helpful in predicting first defaults are not helpful in predicting subsequent default episodes. This has important implications for mortgage investors and servicers as industry foreclosure avoidance efforts intensify.     

A Proportional Hazards Model of Commercial Mortgage Default with Originator Bias

A proportional hazards model with competing risks is specified and is extended to correct for the possibility of originator bias. The model is used to examine the ability of option-theoretic models of mortgage pricing to forecast commercial mortgage defaults. Among the findings, those especially of interest include the influence of contemporaneous loan-to-value and debt-service-coverage ratios on commercial mortgage default probabilities. The paper also finds that option-theoretic models of mortgage pricing are quite capable of producing default estimates that fit the actual default rates well, especially when the model is corrected for originator bias.     

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.     

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.     

信用违约风险传染模型的比较研究

本文试图对几种有代表性的模型进行比较,来分析由于建模方式的不同,而导致的对信用期权定价和对冲的结果的不同.如果将违约风险传染考虑进去,类似德隆帝国崩溃的事件,或许就能避免.     

Valuation of reverse mortgages under (limited) default risk

In this paper, we develop a consistent valuation framework for reverse mortgages based on reduced-form intensity models as used in credit risk modelling. Within our modelling framework, we explicitly calculate the probability that the total loan amount exceeds the house value at termination of the contract and derive the maximum payment(s) which can be made to the homeowner under certain constraints. We apply our results to data from the German market and discuss implications for the design of reverse mortgages from a lender's perspective.     

欧洲高收益债券市场违约风险监管研究

多年以来,欧洲一直是仅次于美国的世界第二大高收益债券市场。除了债券自身信用评级水平之外,欧洲高收益债券违约率的高低与市场监管力度以及宏观金融经济运行状况密切相关。欧洲监管当局把对高收益债券市场的监管重点放在:规范市场信息披露及信用评级标准和行为、保护投资者权益、保持交易行为的规范性和跨国界市场交易衔接处理等方面,这些监管策略的实施对控制市场违约风险起到了积极的作用。欧洲的监管经验对于今后我国高收益债券市场的尝试性推出也极具借鉴意义。     

公司信用债违约风险预警与防范研究

我国债券规模位居世界第二,债券市场已成为企业直接融资的主要渠道;同时我国公司信用债违约频发,违约主体几乎涵盖了全部行业,永煤AAA债券违约事件引发各方关注。在此背景下,本文研究了信用债违约风险预警与防范,搭建了债券违约预警模型:一是深入分析了违约原因,提出了经济下行加剧‘债务-通缩’流动性分层导致再融资困难民企互保引发违约风险串联的观点;二是基于KLR信号分析法,以历史违约主体财报数据为基础构建了上市公司债违约预警模型,抽离出相关指标权重构成预警指标体系,并进行了实证检验;三是基于预警模型,提出加强动态监测、构建债券风险分类管理办法等政策建议。     

A Prepayment Model for the Japanese Mortgage Loan Market: Prepayment-Type-Specific Parametric Model Approach

This paper proposes a framework for construction of a prepayment model suitedto the Japanese mortgage loan market and assesses the validity of thisframework based on an empirical analysis using data from Japan. In thisframework, a model is constructed for each of three prepayment types, namely,`full prepayment', `partial prepayment', and `subrogation', using a parametricproportional hazards model, which was also employed by Schwartz and Torous(1989). Combining these three types of models allows one to take into accountthe effects of partial prepayments, which are frequently used in the Japanesemortgage market, and to simultaneously construct a model for both prepaymentand default. Time-dependent (path-dependent) covariates are introduced intothe model, which are estimated by the maximum likelihood method based on thefull likelihood that takes into account the time-dependence of the covariates.Results of the empirical analysis indicate that the hazard functions differsubstantially depending on the prepayment type. In addition, results indicatethat the fit of the model can be improved by the distinction of prepaymenttypes and the introduction of the market interest rates as path-dependentcovariates.     

An Empirical Estimation of Default Risk of the UK Real Estate Companies

Based on the Black and Scholes (Black, F., and M. Scholes. (1973). The Pricing of Options and Corporate Liabilities, Journal of Political Economy 81, 637–659) and Merton (Merton, R. C. (1974). On the Pricing of Corporate Debt: The Risk Structure of Interest Rates, Journal of Finance 29, 449–470) (BSM) contingent claims model, and KMV Corporation framework, we estimate the distance to default and the “risk neutral” default probabilities for a sample of 112 real estate companies over the period 1980 to 2001. Our empirical results classifies failed and non-failed companies into Type I error, cases that the BSM-type model fails to predict default when it did occur, and Type II error where BSM-type model predicts default when it did not occur. We find that none of the companies belong to the category of Type I error. Type II error is observed in 12 out of 112 companies. These results support the theoretical underpinnings of the BSM-type structural model in that the two driving forces of default are high leverage and high asset volatility.     

Counterparty Risk for Credit Default Swaps: Markov Chain Interacting Intensities Model with Stochastic Intensity

We analyze the counterparty risk for credit default swaps using the Markov chain model of portfolio credit risk of multiple obligors with interacting default intensity processes. The default correlation between the protection seller and underlying entity is modeled by an increment in default intensity upon the occurrence of an external shock event. The arrival of the shock event is a Cox process whose stochastic intensity is assumed to follow an affine diffusion process with jumps. We examine how the correlated default risks between the protection seller and the underlying entity may affect the credit default premium in a credit default swap.