The valuation and securitization of commercial and multifamily mortgages

This paper develops a pricing model capable of accurately valuing commercial mortgages and their mortgage backed securities (MBS). It is the first example in the general literature on mortgage pricing in which the valuation of an MBS is explicitly tied to that of the underlying mortgages, making possible a comparison of the performance of the loans and the securities they back. We have shown that while there are similarities between mortgages and their mortgage backed securities, they act in different ways. In general, it turns out that despite being the more passive asset, the mortgage backed security exhibits the more complicated 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.     

Did the Federal Reserve's MBS purchase program lower mortgage rates?

On November 25, 2008, the Federal Reserve announced it would purchase mortgage-backed securities (MBS). This program affected mortgage rates through three channels: (1) improved market functioning in both primary and secondary mortgage markets, (2) clearer government backing for Fannie Mae and Freddie Mac, and (3) anticipation of portfolio rebalancing effects. We use empirical pricing models for MBS yields and for mortgage rates to measure relative importance of channels: The first two were important during the height of the financial crisis, but the effects of the third depended on market conditions. Overall, the program put significant downward pressure on mortgage rates.     

Semi-analytical MBS Pricing

This paper presents a multi-factor valuation model for fixed-rate callable mortgage backed securities (MBS). The model yields semi-analytic solutions for the value of MBS in the sense that the MBS value is found by solving a system of ordinary differential equations. Instead of modelling the conditional prepayment rate (CPR), as is customary, the pool size is the primary modelling object. It is shown that the value of a single MBS payment due at time t _n can be found by computing two expectations of the pool size at time t _n–1 and t _n respectively. This is a general result independent of any interest rate model. However, if the pool size is specified in a way that makes the expectations solvable using transform methods, semi-analytic pricing formulas are achieved. The affine and quadratic pricing frameworks are combined to get flexible and sophisticated prepayment functions. We show that the model has no problem of generating negative convexity as the spot rate falls, and still be close to a similar non-callable bond when the spot rate rises.     

GSEs,Mortgage Rates,and Secondary Market Activities

Fannie Mae and Freddie Mac are government-sponsored enterprises (GSEs) that securitize mortgages and issue mortgage-backed securities (MBS). In addition, the GSEs are active participants in the secondary mortgage market on behalf of their own investment portfolios. Because these portfolios have grown quite large, portfolio purchases (in addition to MBS issuance) are often thought to be an important force in the mortgage market. Using monthly data from 1993 to 2005 we estimate a VAR model of the relationship between GSE secondary market activities and mortgage interest rate spreads. We find that GSE portfolio purchases have no significant effects on either primary or secondary mortgage rate spreads. Further, we examine GSE activities and mortgage rate spreads in the wake of the 1998 debt crisis, and find that GSE portfolio purchases did little to affect mortgage rates. This empirical finding is robust to alternative identification assumptions and to alternative model and variable specifications.      

住房抵押贷款支持证券定价方法:发展与启示

西方MBS定价方法主要有传统定价法、计量模型定价法、期权调整利差定价法和再融资临界价法.我国在借鉴国外经验对MBS定价的过程中,应充分考虑所处定价环境的差异,采用合理的定价方法.现阶段,我国应加快完善市场利率结构和建设商业银行住房抵押贷款数据库,为MBS的科学定价创造良好条件.     

Planning Your Own Debt

We model the Danish market for mortgage backed securities with a two-factor interest rate model and use a stochastic programming approach to analyse how an individual home-owner should initially compose and subsequently readjust his mortgage in an optimal way. Results show that the 'rules of thumb' used by financial institutions are reasonable, although best suited for more aggressive mortgagors, for whom the delivery option is of some value. More risk-averse investors should also re-adjust frequently, but use more diversified portfolios. Results are insensitive to whether a one- or two-factor model is used, provided the former is suitably calibrated.     

Mortgage Refinancing Activity: An Explanation [1990–2001]

Mortgage refinancing activity reached unprecedented high levels during 1990–2001. Using GARCH to control for heteroskedasticity and separating the data into regimes to control for potential structural changes over time, we estimate a model explaining changes in mortgage refinancing activity over the period studied. We find changes in refinancing activity to be negatively related to current as well as past changes in the 30-year mortgage rate with a declining significant lag over time. Similarly, there is a significant lagged dependent variable with a declining lag. Moreover, mortgage refinancing activity is a substitute for other investments during certain regimes. These results offer evidence that home owners cash out the mortgage for other investments. The lags suggest that the process is delayed for a variety of reasons. The declining lag signals a faster response by consumers. The reasons for a faster response include a consumer perception that interest rates have “bottomed out,” the presence of an increase in consumer sophistication, and improvements in technology and market coordination that facilitate and reduce the cost of the refinancing process.     

Liquidity in a Market for Unique Assets: Specified Pool and To‐Be‐Announced Trading in the Mortgage‐Backed Securities Market

Agency mortgage‐backed securities (MBS) trade simultaneously in a market for specified pools (SPs) and in the to‐be‐announced (TBA) forward market. TBA trading creates liquidity by allowing thousands of different MBS to be traded in a handful of TBA contracts. SPs that are eligible to be traded as TBAs have significantly lower trading costs than other SPs. We present evidence that TBA eligibility, in addition to characteristics of TBA‐eligible SPs, lowers trading costs. We show that dealers hedge SP inventory with TBA trades, and they are more likely to prearrange trades in SPs that are difficult to hedge.     

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.     

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.     

Rational prepayment and the valuation of mortgage-backed securities

This article presents a new model of mortgage prepayments, basedon rational decisions by mortgage holders. These mortgage holdersface heterogeneous transaction costs, which are explicitly modeled.The model is estimated using a version of Hansen's (1982) generalizedmethod of moments, and is shown to capture many of the empiricalfeatures of mortgage prepayment. Estimation results indicatethat mortgage holders act as though they face transaction coststhat far exceed the explicit costs usually incurred on refinancing.They also wait an average of more than a year before refinancing,even when it is optimal to do so. The model fits observed prepaymentbehavior as well as the recent empirical model of Schwartz andTorous (1989). Implications for pricing mortgage-backed securitiesare discussed.     

An Empirical Investigation of Alternative Contingent Claims Models for Pricing Residential Mortgages

Researchers have employed option pricing techniques to analyze mortgage financing and valuation. Alternative models (one-, two-, and three-variable models) employing different variables (short- and long-term interest rates and building value) have been designed to price mortgage securities. No prior research has addressed the question of whether the pricing accuracy of these contingent claims models improves as states increase or whether contingent claims models' valuation abilities generate reasonable estimates of primary mortgage market prices. The articles investigates the relative efficiency of each of these alternative mortgage valuation models in predicting primary market mortgage values. Our results show that a two-variable model (short rate and building value) is the most efficient. Valuation results indicate a positive pricing spread between the primary market and the theoretically estimated value.     

The Cost of Deposit Insurance for Privately Held Banks: A Market Comparable Approach

Previous empirical studies that use an option pricing model to estimate deposit insurance costs have been limited to banks that issue publicly traded securities: a bank's security prices are used to infer its risk characteristics. However, if deposit insurance costs are needed for privately held banks, as would be the case under a system of risk-based insurance premiums, then an alternative method is required. This paper presents a “market comparable” approach for valuing private banks' deposit insurance. The approach first uses information on public depository institutions to identify the statistical relationships between a bank's supervisory accounting data and its risk characteristics derived from equity market data. Second, it uses these relationships to predict the risk characteristics of a private depository institution based on its supervisory accounting data. This approach is applied to over 7000 private banks and thrifts to estimate their risk characteristics and their implied risk-neutral and physical probabilities of insolvency. For the vast majority of institutions, these risk characteristics and insolvency probabilities are within a reasonable range.     

Mortgage Brokers and the Refinancing Transaction: Evidence from CRA Borrowers

This study adds to an emerging literature on the lending practices of mortgage brokers during the run-up in home prices prior to 2006. Following a sample of low— and moderate-income borrowers through the first years following home purchase, the analysis identifies differences in the refinancing transaction associated with the use of mortgage brokers vs. retail lenders. Specifically, the analysis includes measures of the refinancing process, including whether the lender initiated contact with the borrower, whether the terms of the mortgage changed at closing, and the level of borrower satisfaction in hindsight. Care must be taken in extrapolating from this sample to the broader mortgage market, as all borrowers refinanced out of 30-year fixed-rate purchase mortgages in the Community Advantage Program (CAP). Nevertheless, analysis of this sample offers unique insight into borrowers’ interactions with mortgage brokers during the refinancing transaction. Origination with a mortgage broker, compared with origination through a retail lender, is associated with both a less satisfactory refinancing process and a higher likelihood of refinancing into an adjustable-rate mortgage (ARM).     

Are covered bonds different from securitization bonds? A comparative analysis of credit spreads

This study compares credit spreads and pricing determinants of securitization vis-à-vis covered bonds. Our analysis reveals that although ratings are the most important pricing determinant for asset-backed securities (ABS) and mortgage-backed securities (MBS) investors place relatively more importance on contractual, macroeconomic and banks' characteristics rather than ratings in pricing covered bonds. We find evidence of a mispricing effect in structured finance markets: ABS and MBS have higher credit spreads than similarly rated public-covered bonds and mortgage-covered bonds and security prices reflect information beyond credit ratings. We find no evidence of borrowing costs affecting banks' choice between securitization and covered bonds.     

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.     

Is refinancing solely motivated by misappropriation?

Misappropriation has become the accepted explanation for the refinancing behavior of Chinese listed companies, although the evidence in support of such an explanation is worthy of further discussion. We argue that if a planned refinancing exercise does not become a reality, post-refinancing performance depends on the initial motivation for refinancing, i.e. misappropriation or the maximization of firm value. The success and failure samples provided by the approval system of the Chinese securities market provide us with a natural laboratory in which to distinguish between these two possible motivations for the refinancing behavior of Chinese listed firms. The results show the post-refinancing performance of firms in the success sample to be significantly better than the performance in the failure sample, with the difference even more significant when larger agency costs or more financial constraints exist. These findings indicate that Chinese listed companies do not engage in refinancing for misappropriation purposes alone. Rather, refinancing is more likely to be a rational choice made in full consideration of the costs and benefits. This paper provides new ideas for reexamining the motivations for the refinancing behavior of China’s listed firms. It also has one major policy implication. That is, relaxing and/or simplifying the country’s refinancing regulations could help to improve the efficiency of resource allocation in the Chinese securities market.     

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.     

Using Tucker’s theorem of the alternative to simplify,review and expand discrete arbitrage theory

For valuing derivatives and other assets in securities and commodities markets, arbitrage pricing theory has been a major approach for decades. This paper derives fundamental arbitrage pricing results in finite dimensions in a simple unified framework using Tucker’s theorem of the alternative. Frictionless results, that is perfect market results, plus imperfect market results such as those with dividends, periodic interest payments, transaction costs, different interest rates for lending and borrowing, shorting costs and constrained short selling are presented. While the results are mostly known and appear in various places, our contribution is to present them in a coherent and comprehensive fashion with very simple proofs. The analysis yields a simple procedure to prove new results and some are presented for cases with imperfect market frictions.