Measuring investment performance with a stochastic parameter regression model

This paper develops a generalization of the Hildreth and Houck (1968) random coefficient model for use in evaluating the macroforecasting ability of portfolio managers. Most studies have assumed that astute managers ignore the strength of the market trend and create a binary portfolio beta with one value during up markets and a lower value during down markets. In contrast, this paper examines a model in which the superior manager adjusts beta period by period according to changing market conditions. The findings indicate that portfolio managers are not superior macroforecasters.     

Mortgage Termination: An Empirical Hazard Model with a Stochastic Term Structure

Pricing for mortgage and mortgage-backed securities is complicated due to the stochastic and interdependent nature of prepayment and default risks. This paper presents a unified economic model of the contingent claims and competing risks of mortgage termination by prepayment and default. I adopt a proportional hazard framework to analyze these competing and interdependent risks in a model with time-varying covariates. The paper incorporates a stochastic interest rate model into the hazard function for prepayment. The empirical results reported in the paper provide new evidence about the ruthlessness of default and prepayment behavior and the sensitivity of these decisions to demographic as well as financial phenomena. The results also illustrate that evaluating the interest rate contingent claims with a stochastic term structure has effects on predicting not only the mortgage prepayment behavior but also the mortgage default behavior.     

Prepayment and the Valuation of Mortgage-Backed Securities

This paper puts forward a valuation framework for mortgage-backed securities. Rather than imposing an optimal, value-minimizing call condition, we assume that at each point in time there exists a probability of prepaying; this conditional probability depends upon the prevailing state of the economy. To implement our valuation procedure, we use maximum-likelihood techniques to estimate a prepayment function in light of recent aggregate GNMA prepayment experience. By integrating this empirical prepayment function into our valuation framework, we provide a complete model to value mortgage-backed securities.     

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.     

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.     

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.     

Lapse rate modeling: a rational expectation approach

The surrender option embedded in many life insurance products is a clause that allows policyholders to terminate the contract early. Pricing techniques based on the American Contingent Claim (ACC) theory are often used, though the actual policyholders' behavior is far from optimal. Inspired by many prepayment models for mortgage backed securities, this paper builds a Rational Expectation (RE) model describing the policyholders' behavior in lapsing the contract. A market model with stochastic interest rates is considered, and the pricing is carried out through numerical approximation of the corresponding two-space-dimensional parabolic partial differential equation. Extensive numerical experiments show the differences in terms of pricing and interest rate elasticity between the ACC and RE approaches as well as the sensitivity of the contract price with respect to changes in the policyholders' behavior.     

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.     

Characteristics of Mortgage Terminations: an Analysis of a Loan-Level Dataset

Understanding mortgage termination behavior is crucial for valuating mortgage-backed securities. Analyzing a unique loan-level dataset, this study examines the characteristics of mortgage prepayment and default behaviors in the Korean housing and housing finance markets. We also analyze mortgage termination behaviors across regions, loan purposes, and periods. The results suggest that the prepayment rate of fixed-rate mortgages (FRMs) and the ratio of adjustable-rate mortgages to FRMs can provide meaningful signals for the Korean household economy. Although the macro-prudential policies pertaining to the loan-to-value ratio (LTV) and debt-to-income ratio (DTI) are very effective, their effects can vary depending on the region or loan purpose. Furthermore, the DTI and credit score cannot always identify the default risks of mortgages not intended for housing purchases even though such mortgages are more vulnerable to macroeconomic changes. The observed changes in default behavior indicate that the government’s policies to promote fixed-rate loans have achieved a certain degree of success.     

Valuation of GNMA Mortgage-Backed Securities

GNMA mortgage-backed pass-through securities are supported by pools of amortizing, callable loans. Additionally, mortgagors often prepay their loans when the market interest rate is above the coupon rate of their loans. This paper develops a model for pricing GNMA securities and uses it to examine the impact of the amortization, call, and prepayment features on the prices, risks and expected returns of GNMA's. The amortization and prepayment features each have a positive effect on price, while the call feature has a negative impact. All three features reduce a GNMA security's interest rate risk and, consequently, its expected return.     

Time-Varying Mortgage Prepayment Penalties

Recent empirical findings reveal that prepayment decisions of commercial property owners are slower than predicted by the pure options-pricing model (OPM). Borrower decisions appearing slow, however, may be quite rational when prepayment penalties of a time-varying nature are incorporated into the OPM. This article uses a competing risks OPM, adjusted for each of four different categories of prepayment penalties, to analyze borrower prepayment behavior. We find the value of delaying prepayment is often higher for mortgages with declining-rate penalties than for mortgages with static-rate penalties, frequently requiring a substantially higher interest rate spread to trigger a refinance. Multifamily loan prepayment records reveal the type of prepayment pattern that the adjusted OPM indicate should occur, reducing the gap between empirical findings and theoretical predictions. The results have implications for the specification of regressions fit to historical data, for the pricing of newly originated commercial mortgages, and for pricing in the single-family market where prepayment penalties are reemerging.     

Unobservable heterogeneity and rational learning: Pool-specific versus generic mortgage-backed security prices

Previous mortgage prepayment and valuation models assume that two mortgage pools with the same observable characteristics should behave indistinguishably. However, even pools with apparently identical characteristics often exhibit markedly different prepayment behavior. The sources of this heterogeneity may be unobservable, but we can infer information about a pool from its prepayment behavior over time. This article develops a methodology for using this information to calculate pool-specific mortgage-backed security prices. Knowledge of these prices is important both for portfolio valuation and for determining the cheapest pool to deliver when selling mortgagebacked securities. We find that unobservable heterogeneity between mortgage pools is statistically significant, and that pool-specific prices, calculated for a sample of outwardly identical mortgage pools between 1983 and 1989, may differ greatly from any single representative price.     

What Drives Default and Prepayment on Subprime Auto Loans?

This paper uses novel data on the performance of loan pools underlying asset-backed securities to estimate a competing risks model of default and prepayment on subprime automobile loans. We find that prepayment rates increase rapidly with loan age but are not affected by prevailing market interest rates. Default rates are much more sensitive to aggregate shocks than are prepayment rates. Increases in unemployment precede increases in default rates, suggesting that defaults on subprime automobile loans are driven largely by shocks to household liquidity. There are significant differences in the default and prepayment rates faced by different subprime lenders. Those lenders that charge the highest interest rates experience the highest default rates, but also experience somewhat lower prepayment rates. We conjecture that there is substantial heterogeneity among subprime borrowers, and that different lenders target different segments of the subprime market. Because of their higher default rates, loans that carry the highest interest rates do not appear to yield the highest expected returns.     

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.     

Microfoundations of a mortgage prepayment function

This article focuses on the following question: how much of an interest rate decline is needed to justify refinancing a typical home mortgage? Modern option pricing theory is used to answer the question; this theory indicates that the answer depends upon several factors, which include the volatility of interest rates and the expected holding period of the borrower. The analysis suggests that the commonly espoused “rule of thumb” refinance if the interest rate declines by 200 basis points — is a fair approximation to the more precisely derived differential for many households. We also construct the prepayment behavior of a pool of mortgages in which the expected holding periods of the borrowers in the pool vary. The prepayment behavior of this simulated pool is used to generate a series of empirically testable hypotheses regarding the likely shape of an actual prepayment function and its determinants. Finally, actual prepayment data are used to estimate a hazard function that explains prepayment behavior. We find that the estimated model understates prepayment behavior relative to that predicted by the simulation model, which suggests that the simple option pricing model is not adequate to explain aggregate prepayment behavior.     

A Top-Down Approach for Asset-Backed Securities: A Consistent Way of Managing Prepayment, Default and Interest Rate Risks

We define a new approach to manage prepayment, default and interest rate risks simultaneously in some standard asset-backed securities structures. We propose a parsimonious top-down approach, by modeling directly the portfolio loss process and the amortization process. Both are correlated to interest rates. The methodology is specified for sequential- and pro-rata pay bonds (ABS, CMO, CDO of ABS), cash or synthetic. We prove analytical formulas to price all tranches, under and without the simplifying assumption that amortization occurs in the most senior tranche only. The model behavior is illustrated through the empirical analysis of an actual synthetic ABS trade.     

Household Income, Termination Risk and Mortgage Pricing

The premium embedded in home mortgage loans to compensate investors for their exposure to prepayment risk is a significant component of the cost of home mortgage lending. Moreover, there is some reason to believe that prepayment risk may be lower for loans to lower-income housing borrowers, especially those that are first-time home owners. If so, investor recognition of this advantage should facilitate greater willingness to acquire portfolios of lower-income housing loans, and encourage more competitive pricing in this segment of the market. This study investigates the possibility of differential mortgage prepayment behavior between lower-income home owners and non-low income home owners. The investigation relies on samples of the American Housing Survey spanning ten years of experience from 1985 to 1995. We find no significant difference between the termination or refinancing behavior of non-low income and low-income households. This result is robust to a number of alternative specifications such as restricting the low-income test group to non-moving households and to first-time owners. The same conclusions are derived from both aggregate prepayment rates and from analysis of individual household prepayment behavior.     

Rational Prepayments and the Valuation of Collateralized Mortgage Obligations

This article presents a procedure for evaluating collateralized mortgage obligation (CMO) tranches. The solution procedure is in the spirit of a dynamic programming problem in which an individual mortgagor's decision to prepay is the feedback control variable―the mortgagor seeks to minimize the value of the mortgage subject to refinancing costs. We employ a two-step procedure to solve this dynamic programming problem. The first step uses an implicit finite difference backward solution procedure to determine the “optimal” prepayment boundary for a class of mortgagors, each of whom confronts the same proportional refinancing cost. This step is repeated for several different classes of mortgagors that differ in the level of refinancing costs that they confront. The outcome of this first step is a series of prepayment boundaries―one set of boundaries for each level of refinancing costs (i.e., one set of boundaries for each refinancing cost category of mortgagors). In the second step, the prepayment boundaries determined in the first step are used in conjunction with Monte Carlo simulation to value the CMO tranches. The essence of the second step is that when the simulated interest rate hits the boundary for a particular class, it triggers a prepayment scenario for that class of mortgagors. We conduct extensive sensitivity analysis to determine the robustness of this approach (and our solution procedure) to alternative single-factor models of the term structure of interest rates and to alternative specifications of the distribution of refinancing cost levels confronted by mortgagors. The sensitivity analysis indicates that CMO tranche valuation is not particularly sensitive to alternative models of the term structure so long as the models are consistent with the current yield curve, but, even when alternative specifications of the refinancing cost categories generate nearly identical values for the collateral underlying the CMO (i.e., the generic mortgage-backed securities), the resulting tranche values can differ widely between the two specifications. The results point out the importance of accurate estimation of the distribution of refinancing costs when the rational valuation model is used for the analysis of CMO tranches.     

住房抵押贷款提前还贷风险管理研究

从现代金融和风险管理角度看,住房抵押贷款提前还贷对商业银行是一种期权性风险,对其收取违约金并非国际惯例,也并不是有效的风险补偿方式。商业银行应适应市场竞争需要,接受风险转嫁并提供风险管理服务,运用风险定价技术在按揭交易价格中对提前还贷风险进行补偿。对于已承担的风险,商业银行应构建抵押贷款提前还贷的数据库,通过表内对冲和市场对冲,推出多样化的住房抵押贷款方式,积极推进住房抵押贷款证券化,从而最终增强银行的盈利来源和核心竞争力。     

Derivative mortgage securities: An overview

Derivative mortgage securities have proliferated since planned amortization and floating rate CMO classes were introduced in late 1986. Other recently created derivative securities include reverse floaters and deep-discount bonds of CMOs, CMO residuals, and stripped and senior/subordinated passthroughs. These securities, which are derived from fixed-rate mortgages, were created to meet investor demands for maturity certainly, interest rate and prepayment hedging, and enhanced credit. The rapid growth of derivative securities reflects expansion of the investor base for fixed-rate mortgages. It also suggests that these mortgages will continue to be a viable housing finance instrument in a volatile interest rate environment. For the future, the increased creation of derivative securities will make the secondary mortgage market more efficient, facilitating the funding of fixed-rate mortgage originations.The substance of this paper was originally written in late 1987 and many of the specific data reflect that time period.