Prepayment Model Research Articles

Valuation of Mortgages by Using Lévy Models

In a mortgage valuation model, the early termination (i.e., prepayment and default) hazard rates and the recovery rate can be specified as multivariate affine functions that include the correlated stochastic state variables. For good capturing of the distributions for state variables, we specify that the state variables follow Lévy models. Accordingly, the early termination hazard rates and the recovery rate also follow Lévy models. Three popular Lévy models, the normal, Variance Gamma (VG), and Negative Inverse Normal (NIG), were used to obtain the closed-form pricing formula for a mortgage. We also conduct numerical applications. Our results reveal the following findings: first, VG model is better than the normal and NIG models in fitting the actual distributions of the interest rate and the housing return rate. Thus, mortgage valuation using a VG model should be better than that using the other two models. Second, the mortgage value estimated by the normal model is the lowest among the three Lévy models. Third, a prepayment hazard rate with a deterministic value (e.g., using the PSA prepayment model) could result in an unreasonable mortgage duration. Fourth, the mortgage convexity calculated by the normal model is higher than that in the other two Lévy models. Our general pricing formula for a mortgage as described in this study can help market participants accurately value mortgages and effectively manage their risks.

A comparative study on determinants of housing mortgage prepayment of individual borrowers

This paper examines how the macroeconomic environment affects the determinants of prepayment of mortgage loans from October 2004 to February 2020. For more accurate analysis, the authors define the timing of prepayment not only before the loan maturity but also at the time when 50% or more of the loan principal is repaid. The results show that, during the global financial crisis as well as the recent period of low interest rates, macroeconomic variables such as interest rate spreads and housing prices have a different effect compared to the normal situation. Also, significant explanatory variables, such as debt to income (DTI) ratio, loan amount ratio and poor credit score, have different effects depending on the macroenvironment. On the other hand, in all periods, the possibility of prepayment increases as comprehensive loan to value (CLTV) increases, and the younger the age, the shorter the loan maturity. The results suggest that, in the case of ultralong (40 years) mortgage loans recently introduced to support young people purchasing houses, the prepayment risk can be, at least partially, migrated by offsetting the increase in prepayment by young people and the decrease in prepayment due to long loan maturity. In addition, this study confirms that the accelerated time failure model compared to the logit model and COX proportional risk model has the potential to be more appropriate as a prepayment model for individual borrower analysis in terms of the explanatory power.

Machine Learning–Based Systematic Investing in Agency Mortgage-Backed Securities

With a total outstanding balance of more than $8 trillion as of this writing, agency mortgage-backed securities (MBS) represent the second largest segment of the US bond market and the second most liquid fixed-income market after US Treasuries. Institutional investors have long participated in this market to take advantage of its attractive spread over US Treasuries, low credit risk, low transaction cost, and the ability to transact large quantities with ease. MBS are made of individual mortgages extended to US homeowners. The ability for a homeowner to refinance at any point introduces complexity in prepayment analysis and investing in the MBS sector. Traditional prepayment modeling has been able to capture many of the relationships between prepayments and related factors such as the level of interest rates and the value of the embedded prepayment option, yet the manual nature of variable construction and sheer amount of available data make it difficult to capture the dynamics of extremely complex systems. The long history and large amount of data available in MBS make it a prime candidate to leverage machine learning (ML) algorithms to better explain complex relationships between various macro- and microeconomic factors and MBS prepayments. The authors propose a systematic investment strategy using an ML-based mortgage prepayment model approach combined with a coupon allocation optimization model to create an optimal portfolio to capture alpha vs. a benchmark.

Prepayment Model of Supply Chain Financing Based on Internet of Things and Machine Learning Algorithm

Nowadays, the relationship between all kinds of things is constantly strengthened, and the regional restrictions on things are also constantly weakened, especially in the aspect of trade. In the past, people could only buy some basic goods in a relatively small area if they wanted to buy them in a relatively small area, but now the situation is very different. People's dependence on traders is gradually decreasing; that is to say, the traditional advantages of traders are gradually losing. Particularly, in today's fierce competition, survival of the fittest, and limited profits, the entire trade industry is facing a lot of impacts, not to mention the survival of traders relying on this industry. Therefore, traders must think of a new way to adapt to the characteristics of the new era, to continue to make profits and maintain their own survival. In fact, for the whole industry, this is also the most urgent problem to be solved. This study mainly explores the above problems and puts forward some feasible methods to solve the problems, hoping to cause some thinking of the industry personnel, so that they can modify and adjust their working mode. In addition, it should be emphasized that the mode of using Internet of things and machine learning to achieve the purpose of innovation is of great practical significance.

Financial and Geographic Barriers to Health Care Access in Kenya: The Quest towards Universal Health Coverage

Abstract Background: Access to health care services without being plunged into financial hardship is a life blood of the Universal Health Coverage. Kenya's health sector is heavily dependent on out of pocket health expenditure. This model of health financing is inequitable and leads to underutilization of the much needed health care services. Majority of Kenyans travel for longer distances to access health care services. The geographic access barrier is linked to delayed care, missed appointments, delayed medication and undue loss of life. This study examines the correlates of financial and geographic health care access barriers in the UHC implementing Counties in Kenya. Methodology: The study used a cross-sectional data collected from 249 respondents using exit interviews at the health facilities drawn from the Kenya Master Health Facility List (KMHL). A multivariate log it regression model was used to analyze the predictors of probability of failure to access health care services owing to prohibitive health care and transport costs. Results: High out-of-pocket monthly expenditure on medicine; wider proximity, higher transportation cost and a longer traveling time to a health facility increases the probability of not seeking medical treatment owing to prohibitive health care and transportation costs. These factors thus, acts as key barriers to health care access. Conclusion: Financial and geographic access barriers negatively impact on health care access. To hasten the realization of the Universal Health Coverage, prepayment models such as use of taxes and insurance should be pursued.

Editor’s Letter

1. Stanley J. Kon 1. Editor The performance of security selection within the Agency mortgage-backed securities market is primarily dependent on the quality of the trader’s prepayment model. Each prepayment wave has unique characteristics and an opportunity for dynamic adaptation. We begin

Rise of the Machines: Application of Machine Learning to Mortgage Prepayment Modeling

Key to the valuation of agency residential mortgage-backed securities (MBSs) is the modeling of voluntary prepayment and default behaviors of the underlying borrowers in the mortgage pool. The proliferation of pool- and loan-level data coupled with access to advanced machine learning algorithms has opened the door to the application of machine learning to mortgage prepayment modeling. The modular prepayment model, one that relies on defined functions to predict mortgage prepayment, has dominated the MBS market nearly since its inception. However, machine learning models are beginning to make inroads and, in some cases, are replacing traditional modular prepayment models. The modular and machine learning model differ in the following ways: In the case of modular prepayment models, either added or multiplicative, the modeler defines the functional form of each feature as well as the “tuning” of the parameters passed to each. Machine learning or “second generation” mortgage prepayment models differ in the sense that the modeler “tunes” the hyperparameters that determine the bias variance tradeoff while the machine determines the functional form of each feature of the model. In this article, the authors propose a machine learning mortgage prepayment model using a boosted gradient classifier, trained at the loan level and generalized to the pool level. A gradient boosted classifier is a tree-based model using an ensemble of weak learners to create a strong committee for prediction.

Rational Attention Allocation in the Mortgage Market

We propose a structural mortgage prepayment model, where mortgage holders have to allocate costly attention to implement prepayment decisions, and apply the model to US prime mortgages. Our empirical results suggest that commonly observed refinancing mistakes, such as choosing a financially suboptimal refinancing rate by waiting for too long, can be optimal responses of borrowers who allocate their attention rationally. We find that financial sophistication and experience in refinancing reduce costs for attention, while additional financial obligations cause the opposite. Compared to a situation without costs for attention, we estimate that the rational allocation of costly attention increases the value of liabilities by $4,214 for a median mortgage. We find that after the Great Financial Crisis, both the costs for attention as well as the impact of financial sophistication, experience in refinancing and additional financial obligations on the costs for attention increase. The increase of the costs for attention leads to an additional increase of the value of liabilities of 15% after the Great Financial Crisis. Our results have implications for the effectiveness of monetary policy transmission, especially, following an economic crisis.

Designing and Estimating a Prepayment Model for Callable Mortgage Bonds

Designing and Estimating a Prepayment Model for Callable Mortgage Bonds

Rank-Based Error Tracking for Agency MBS Prepayment Models

Mode testing, also called error tracking, is a key requirement for collateral behavior forecasting models in securitized product, including models of prepayment, default, response, utilization, etc. The high dimensionality and statistical noise associated with agency mortgage-backed securities prepayment behavior make error tracking a complex task. The traditional method focuses on single dimension, for example, along vintage coupon, and does not provide a clear measure of model accuracy and effectiveness. The new method, a rank-based error-tracking methodology, provides an efficient and comprehensive approach to measure model performance. It provides a clear definition of accuracy-which allows clear measure to compare among models. This is superior to the existing one-dimensional method, and other supplement methods (e.g., lift curve method for loans). We discuss these issues as well as applicable statistical theory, and potential applications. <b>TOPICS:</b>MBS and residential mortgage loans, factor-based models <b>Key Findings</b> • The proposed ranked-based error tracking provides a comprehensive and consistent measure for model performance across macroeconomic environment and across pool/loan attributes, superior to the prevailing one-dimensional error-tracking methodology. • Two key measures are the steepness and accuracy of the ranking curve. The steepness measures quantify the model’s ability differentiating across macro and pool variables. The accuracy measures quantify the model’s ability forecasting the prepayment intensity. • The rank-based methodology can be applied to any selected sample pool universe and performance periods. It can be systematically used for model review and model comparison.

Agency MBS Prepayment Model Using Neural Networks

The authors apply deep neural networks, a type of machine learning method, to model agency mortgage-backed security (MBS) 30-year, fixed-rate pool prepayment behaviors. The neural networks model (NNM) is able to produce highly accurate model fits to the historical prepayment patterns as well as accurate sensitivities to economic and pool-level risk factors. These results are comparable with model results and intuitions obtained from a traditional agency pool-level prepayment model that is in production and was built via many iterations of trial and error over many months and years. This example shows NNM can process large datasets efficiently, capture very complex prepayment patterns, and model large group of risk factors that are highly nonlinear and interactive. The authors also examine various potential shortcomings of this approach, including nontransparency/“black-box” issues, model overfitting, and regime shift issues.

A Practical Guide to the Validation of Models Used to Value, Hedge and Forecast Mortgage Servicing Assets (MSAs): Part I - Process Verification

Mortgage servicing assets are complex option-embedded financial instruments. Their values are volatile and highly exposed to interest rate risk. Much of the blame for the financial crisis of 2008 has been placed on the mortgage industry. This led to the resurrection of the risk-sharing bond concept in 2013. That is when government-sponsored enterprises (GSEs) started using credit-risk-transfer (CRT) transactions to reduce their exposure to credit risk. Mortgage put-back risk manifested itself in giant lawsuits from mortgage bond investors demanding banks to repurchase loans. Extremely low interest rates along with Federal Reserve agency MBS purchase program forced modelers to re-think their term structure models, prepayment models, primary-secondary spread (pss) models, etc. Poor performance of the prepayment models put MSR hedging strategies to the real model risk test. This paper series will examine the state of the mortgage industry and its organization while proposing a practical approach to the validation of models used to price, forecast, and hedge mortgage servicing assets. It is our hope that what is outlined in this paper will help model validators provide effective challenge and strengthen model risk management practices. In Part I, we will focus on the validation of inputs and processing components.

Macroeconomic-Driven Prepayment Risk and the Valuation of Mortgage-Backed Securities

We develop a three-factor no-arbitrage model for valuing mortgage-backed securities in which we solve for the implied prepayment function from the cross-section of market prices. This model closely fits the cross-section of mortgage-backed security prices without needing to specify an econometric prepayment model. We find that implied prepayments are generally higher than actual prepayments, providing direct evidence of significant macroeconomic-driven prepayment risk premiums in mortgage-backed security prices. We also find evidence that mortgage-backed security prices were significantly affected by Fannie Mae credit risk and the Federal Reserve’s quantitative easing programs. Received May 10, 2016; editorial decision September 22, 2017 by Editor Stijn Van Nieuwerburgh.

Loan Fair Value Approaches Revisited

In this paper we discuss practices for fair value estimation of banking book items. While fair value principles are not new they have gained in importance recently with new accounting regulations (e.g., IFRS 9) and banks are also considering market best practices to disclose banking book valuations focusing on market implied views rather than potentially biased internal views. A core part of the fair value estimation is the extraction of the risk-neutral market implied view on risk spreads using either directly observable or approximate market spreads. Such extraction can be based on the available credit markets and one can either extract a spread or premia directly from the market or start with a real-world model of credit risk as the basis and add a market induced risk premia. In the latter case there is the benefit of relating real-world expected loss models to risk-neutral. Regardless of approach - using the actual spread or risk premium extracted from the market in discounting of cash flows is of course central in fair value and the foundation of the market valuation principle. As for the bulk of the banking book items there are no active quote markets the fair value estimation often uses the discounted cash flow principle similar to bonds. Loans may however have rating or credit state dependent cash flow features that require a valuation using a state transition matrix setting. Similarly, loans may be exposed to statistical prepayment models that require adjustments to simple bond valuation schemes. In our valuation scheme we strip the cash flows of financial engineering valued embedded options and value such embedded optionality separately. This definition of the valuation cash flows is consistent with the new regulation for interest rate risk in the banking book which is an advantage as such banking book cash flows should already be available in banks.

Relationship between risk assessment and payment models in Swedish Public Dental Service: a prospective study

BackgroundTo a) compare risk categories in patients selecting a capitation payment (CP) model with those in fee-for-service (FFS), b) determine the 3-year caries increment in the two groups, and c) compare the amount of delivered preventive care in the two groups.MethodsA comprehensive risk assessment was carried out in 1295 young adults attending eight Public Dental Clinics in the Scania region and 75% could be re-examined after 3 years; 615 had selected the CP model and 310 the traditional FFS. Caries was scored according to WHO and data concerning preventive care was extracted from the dental records.ResultsMore patients in the low risk category preferred the CP model (74% vs. 26%) while >80% with high risk selected FFS. The baseline caries level was significantly higher in the FFS group as well as the 3-year caries increment (1.6 vs. 0.8 DFS: p < 0.05). The amount of additional preventive care delivered to each patient was generally lower in the FFS model; it was most frequent among patients with “some” risk in the CP model (83.8%) while the lowest delivery rates were found among low risk patients in the FFS system (32.4%).ConclusionsYoung adults in public dental care with low risk preferred the prepaid model while those in the higher risk categories selected fee-for-service. As more additional preventive care was delivered to patients in the subscribed care, oral health planners and decision makers should be aware of the fact that capitation payment models may enhance inequalities in dental health over time.

Reverse Engineering of Prepayment Functions andthe Potential Applications for MSRs and IOs Valuation

By reverse engineering the different projected prepayment curves submitted by several banks to Bloomberg, the authors were able to develop a model with six parameters, representative of these projections. Some of the parameters in our model must have different interpretations across banks. Mortgage servicing rights and interest only securities are the most affected securities by prepayments, and the model shows that there is a need for further research to refine projections of prepayments. The main users of this reverse-engineered prepayment model will be investors and servicers of mortgage-backed securities. The model could be uploaded on Bloomberg and be interactive, in order to allow different parties to enter their own assumptions and obtain their own prepayment projections.

Additional Market Risk Shocks: Prepayment Uncertainty and Option-Adjusted Spreads

Assessments of market risk for economic or regulatory capital typically involve calculating a portfolio’s sensitivity to key risk factor movements. Historically, practitioners have focused on two classical sources of risk, adverse changes in interest rates and volatility. As stress testing has evolved, additional risk factors have been identified, including several specific to fixed-income securities with embedded optionality. These include changes in prepayment rates or any of several other market risk factors, which affect option-adjusted spreads (OAS). We describe an empirical framework for generating shocks to prepayment rates and mortgage security OAS, which are consistent with simultaneous movements in other key risk factors, including the term structure of interest rates and implied volatility. Our prepayment rate shocks capture model misspecification and are calculated using historical performance data from multiple vendor prepayment models. These shocks are well defined, but capture only a portion of prepayment model error. Mortgage security OAS serves as a broader measure of model error, which encompasses both, model misspecification and forecasting errors as well as credit and liquidity risk. Our OAS shocks are calculated using historical six-month changes in spreads derived from multiple vendor quotes.

Efficient Value at Risk Estimation for Mortgage-Backed Securities

We develop an efficient Monte Carlo simulation-based methodology for value at risk (VaR) and sensitivity analysis of mortgage-backed securities (MBS) that employs an importance sampling technique developed for quadratic VaR models. Our approach, whose validity is derived from a fundamental result in perturbation analysis, is applicable to any analytic interest rate and prepayment model, and more generally to any path-dependent cashflows that admit analytic gradients. We compare the accuracy and computational performance of our VaR estimators with those obtained via finite-difference gradient approximation schemes.

A Stochastic U.S. House Price Model for Valuing Residential Mortgages and Other House Price–Dependent Assets

House prices are an important input to default and prepayment models used to project residential mortgage cash flows. I present a stochastic model of U.S. house prices to be used in valuing residential mortgages and other house price–dependent assets. The model generates a forecast of the full distribution of future house prices over long time horizons. The fundamental value of house prices is modeled as a function of rental rates and interest rates. House prices move relative to fundamental value based on serial correlation and mean-reversion dynamics. A 1,000-path Monte Carlo simulation of future house prices results in a positively sloped term structure of the expected volatility of house prices as of December 31, 2011. This slope flattens over certain horizons because of mean-reversion dynamics but steepens again because of the relation between house prices and interest rates. The model accounts for the changing relation between house prices and interest rates, and the importance of this relation in measuring the interest rate risk of mortgages is demonstrated. <b>TOPICS:</b>Real estate, MBS and residential mortgage loans, simulations, developed markets [US]

Rate-Related MBS Prepayment and Fallout Behavior Model with Quasi-Simulation and Empirical Restrictions

Prepayment behavior is traditionally a significant component of the MBS pricing and hedging models. Since U.S. financial crises of 2007-2009 highlighted the danger of the overreliance on the past experience, which may not be a proper indication of the future performance, there is a constant search of more relevant models aimed to overcome limitations of the historical analysis. We introduce the following innovation in the prepayment behavior forecasting: (a) combine empirical and theoretical approach to the forecasting, simulating the rate path, while predicting the target rate with an empirical model (b) introduce macro-variables into target rate forecast part of the analysis. We find that forecasting the mortgage rates with macro-variables is plausible in 1,3,6,9 and 12 month periods. We further establish methodology of the path forecasting and prepayment rates calculation based upon falling rate environment and rising rate environment examples. We observe interesting effects, suggesting high probability of loan fallout in the rising rate environment due to the intermediate rate fluctuations. We also notice signs of early determination of the fallout/prepayment decision. We suggest our finding are a promising addition to the established prepayment/fallout models.