Prepayment Risk in Adjustable Rate Mortgages Subject to Initial Year Discounts: Some New Evidence

This paper uses microlevel data to examine recent prepayment performance of adjustable rate mortgages (ARMs) employing the competing risk methodology developed by Deng, Quigley and Van Order (2000). We find support for the teaser rate and adjustment date effects implied by the theoretical model of Kau et al. (1993). In addition, we find that teased ARMs bear prepayment risk related to their discount, contrary to results reported by VanderHoff (1996) and Green and Shilling (1997). Finally, and contrary to the usual finding for fixed-rate mortgages, we find that loan age has a negative effect on prepayment risk for ARMs, consistent with the phenomenon that borrowers with high mobility and/or propensity to refinance exit the pool early.     

Adjustable and Fixed Rate Mortgage Termination, Option Values and Local Market Conditions: An Empirical Analysis

This paper analyzes the probabilities of prepayment or default for Fixed Rate Mortgages (FRMs) and Adjustable Rate Mortgages (ARMs). Using data from the period 1985–1992, the analysis indicates that the likelihood of prepayment of thirty year FRMs was determined primarily by house price appreciation and personal income growth and the likelihood of prepayment of fifteen year FRMs was determined primarily by interest rate changes. ARMs were prepaid less frequently than FRMs, were less likely to be prepaid when interest rates declined and defaulted more often than FRMs. The analysis provides evidence that ARM holders are less mobile than FRM holders.     

ARM Wrestling: Valuing Adjustable Rate Mortgages Indexed to the Eleventh District Cost of Funds

This article analyzes adjustable rate mortgages (ARMs) based on the Eleventh District Cost of Funds Index (EDCOFI). The behavior of EDCOFI was examined over the period 1981–1993. Adjustments in this index lag substantially behind term structure fluctuations. Also, the seasonality and days-in-the-month effects noted by previous authors are really symptoms of a January effect . A finite difference valuation algorithm was developed which accounts for all usual ARM contractual features, in addition to the dynamics of EDCOFI. This pricing algorithm allows us to determine endogenously the optimal prepayment strategy for mortgage holders, and hence the value of their prepayment options. The dynamics of EDCOFI give significant value to this option, typically around 0.5% of the remaining principal on the loan.     

A Note on Hybrid Mortgages

We extend previous research on traditional one-year adjustable-rate mortgages (ARMs) by analyzing the performance of 3/27 hybrid instruments. Under this contract innovation, which first appeared in the mid-1990s, note rates are fixed for three years after which they convert to a traditional one-year adjustment schedule with periodic and lifetime caps. We find high rates of prepayment, particularly at time of initial rate adjustment, and relatively high rates of default, as would be consistent with the payment shock that often affects adjustable-rate loans.     

Consumer Welfare Under the Adjustable-Rate Mortgage: Some Empirical Evidence

The theoretical literature on the economics of mortgage choice holds that consumer-borrower preference for the ARM depends largely on the FRM-ARM rate differential. However, there is no empirical evidence as to whether consumers are better off, worse off, or left indifferent with the choice of the ARM relative to the alternative FRM. This paper estimates the windfall gain or loss induced by the FRM-ARM rate differential in a multiperiod setting. The major results are as follows: (1) on the average consumer-borrowers reap windfall gain from the use of ARM, (2) but some individual consumers had windfall loss, (3) consumers with ARMs that have periodic interest-rate caps have significantly higher windfall gain than consumers whose ARMs have no periodic rate caps, and (4) the level of the windfall gain (loss) appears to be correlated with the slope of the yield curve and the level of interest rate.     

Efficiency in the Mortgage Market: The Borrower's Perspective

This paper uses mortgage history data from the Federal Home Loan Mortgage Corporation to analyze the prepayment behavior of homeowners and to test whether borrowers exercise their prepayment options in a manner consistent with contingent claims models. A variety of hazard models are estimated from individual data on more than 6000 mortgages issued during the 1976–1980 period. In these models, it is clear that the extent to which the prepayment option is "in the money" has a strong effect on behavior. However, it is less clear that the option is exercised quite as ruthlessly as the theory predicts.     

Interfirm Bundled Discounts as a Collusive Device

This paper investigates whether and how firms competing in price with homogeneous goods (i.e., Bertrand competitors) can achieve supernormal profits using interfirm bundled discounts. By committing to offering price discounts conditional on the purchase of a specific brand of other differentiated good, the homogeneous good suppliers can separate consumers into distinct groups. Such brand‐specific discounts help the firms relax competition and attain a collusive outcome. Consumers become worse off due to higher effective prices. Our result shows that in oligopolies it is feasible to leverage other's market power without excluding rivals.     

Tariff-mediated network effects versus strategic discounting: Evidence from German mobile telecommunications

Mobile telecommunication operators routinely charge subscribers lower prices for calls on their own network than for calls to other networks (on-net discounts). Studies on tariff-mediated network effects suggest this is due to large operators using on-net discounts to damage smaller rivals. Alternatively, research on strategic discounting suggests that small operators use on-net discounts to advertise with low on-net prices. We test the relative strength of these effects using data on tariff setting in German mobile telecommunications between 2001 and 2009. We find that large operators are more likely to offer tariffs with on-net discounts but there is no consistently significant difference in the magnitude of discounts. Our results suggest that tariff-mediated network effects are the main cause of on-net discounts.     

Pricing Mortgage-Backed Securities: Integrating Optimal Call and Empirical Models of Prepayment

Residential mortgage borrowers frequently appear to behave suboptimally with respect to their mortgage prepayment options. Many borrowers fail to exercise even well-into-the-money options while others prepay when the call option is out-of-the-money. To account for these apparently suboptimal prepayments, the recent trend in mortgage-backed securities research has been away from optimal call valuation models, in which the decision to exercise is determined endoge-nously, in favor of models in which prepayment behavior is exogenously specified based on empirical estimation. This paper develops a rational model of mortgage prepayment which incorporates both types of "non-optimal" prepayment and retains endogenous call. This enables the model to disentangle and compare the separate effects of the interest rate call, impeded by transaction costs, and of non-interest-rate driven prepayment. In addition, by recognizing heterogenous borrower transaction costs, the model presents a way to account more precisely for the varying prepayment lags associated with well-into-the-money call options and to account for the phenomenon of "burnout" within a mortgage pool. The paper includes an empirical test of the unbiasedness of the integrated pricing model by comparing simulated prices from our theoretical model to observed prices on traded Fannie Mae and GNMA securities.     

Prepayment Penalty as a Screening Mechanism for Default and Prepayment Risks

The objective of this article is to offer a theoretical model of asymmetric information to analyze the screening role of prepayment penalty. We consider both default risk and prepayment risk. What makes the role of prepayment penalty interesting and more complicated is that a borrower's contract choice could send conflicting signals to the lender about that borrower's default and prepayment risk type. This is different from earlier theoretical models of mortgage choice under asymmetric information where a certain aspect of the contract (e.g., discount points or loan‐to‐value ratio) is explored as a screening mechanism for a single risk dimension (default risk or prepayment risk) of the borrower type. We show the existence of separating equilibria where different default and prepayment risk types choose contracts with different combinations of prepayment penalty and interest rate. For certain parameter combinations, the model also generates a pooling equilibrium where all borrower types obtain the same contract. Our analysis could offer a partial explanation for the observation that contracts with prepayment penalties are a lot less prevalent than contracts with points.     

Valuing the Mortgage Borrower's Prepayment Option

This paper investigates the value of the prepayment option that normally accompanies a fixed-rate mortgage. Using the two-state option-pricing model developed by Bartter and Rendleman, the paper presents simulations of prepayment option values using several sets of interest rate parameters. The sensitivity of the value of the option to changes in various aspects of the mortgage contract is assessed. Prepayments are not priced separately in the market from the underlying mortgage, so the paper investigates how the inclusion of a prepayment option affects the contract interest rate. Finally, there is reason to believe that any option-pricing model will overestimate the value of a mortgage prepayment option. The size of this bias is assessed indirectly and is found to be rather small.     

Managing the Short-Term Interest Rate Exposure Inherent in Adjustable Rate Mortgage Loans

This paper develops a model for determining the level of, and changes over time in, the short-term interest rate exposure contained in adjustable rate mortgage loans (ARMs). Results of the study indicate that movements in the underlying adjustment index can create both upward-movement or downward-movement interest rate risk for lenders whose ARMs carry rate adjustment limits. The model presented here is useful for designing hedging strategies for ARM loans, and for analyzing the impact of new originations on the interest rate exposure of the ARM portfolio.     

Robust exclusion and market division through loyalty discounts

We show that loyalty discounts create an externality among buyers because each buyer who signs a loyalty discount contract softens competition and raises prices for all buyers. This externality can enable an incumbent to use loyalty discounts to effectively divide the market with its rival and raise prices. If loyalty discounts also include a buyer commitment to buy from the incumbent, then loyalty discounts can also deter entry under conditions in which ordinary exclusive dealing cannot. With or without buyer commitment, loyalty discounts will increase profits while reducing consumer welfare and total welfare as long as enough buyers exist and the entrant does not have too large a cost advantage. These propositions are true even if the entrant is more efficient and the loyalty discounts are above cost and cover less than half the market. We also prove that these propositions hold without assuming economies of scale, downstream competition, buyer switching costs, financial constraints, limits on rival expandability, or any intra-product bundle of contestable and incontestable demand.     

An Arbitrage-Free Estimate of Prepayment Option Prices in Fixed-Rate GNMA Mortgage-Backed Securities

In an efficient market, the no-arbitrage condition implies that the price difference between any two assets must be the market value of all differences in their cash flows. We use this logic to deduce the price of the prepayment option embedded in fixed-rate Government National Mortgage Association (GNMA) mortgage-backed securities. The option price equals the difference between an observed GNMA price and the cost of a synthetic, nonprepayable GNMA constructed from the least expensive portfolio of Treasury securities that exactly replicates the promised GNMA cash flow stream, assuming prepayment is precluded. We regress the option prices on variables found significant in previous prepayment studies, finding that five key regressors explain more than 90% of the prepayment option value in pooled time-series cross-sectional analysis. We also show that the time value of the prepayment option calculated by our method displays a pattern similar to that produced by the Black-Scholes (1973) option pricing model. An additional empirical result is the existence of negative option prices and negative time value of the option prices. We attribute these to the fact that homeowners sometimes exercise their prepayment options when they are out-of-the-money, and to refinancing transaction costs. Our method is independent of assumptions regarding interest rate processes and the homeowner's prepayment behavior, and it provides a benchmark for testing theoretical prepayment models.     

Telemedicine competition,pricing, and technology adoption: Evidence from talk therapists

This paper examines how new telemedicine competitors affected incumbent health care providers during the first waves of COVID-19. Using data from the largest mental health provider search platform in Canada, I show that increased telemedicine competition in a market caused incumbent providers in that market to stop offering income-based discounts to patients. I isolate the causal effect of competition in a difference-in-differences framework, comparing providers before and after a supply shock on the platform that exogenously assigned some markets new telemedicine search results. I find that higher-quality providers are more likely to stop income-based discounts when facing new telemedicine entrants, while lower-quality providers are more likely to exit the platform, which is consistent with telemedicine providers competing for more price-sensitive patients. The results suggest that expanding telemedicine options had a heterogeneous effect on the affordability of care.     

Experimenting with purchase history based price discrimination

Many purchases of differentiated goods are repeated, giving sellers the opportunity to engage in price discrimination based upon the shopper's previous behavior by either offering loyalty discounts to repeat buyers or introductory rates to new customers. Recent theoretical work suggests that loyalty discounts can be profitable to sellers when customer preferences are not stationary and sellers can pre-commit to prices for repeat buyers, but otherwise returning customers can be expected to pay the same or more than new buyers. This paper reports behavior in controlled laboratory experiments designed to empirically test the impact of these factors on pricing strategies. The results generally support the comparative static predictions of the theoretical model. When customer preferences are fixed over time, sellers attempt to lure customers from their rival. Price pre-commitment for repeat shoppers when buyer preferences vary over time resulted in modest loyalty pricing, but the discounts are not as prevalent as predicted as sellers rarely price below cost. Behaviorally, price pre-commitment to loyal customers is found to reduce prices overall.     

Adjustable-Rate Mortgages, Economic Fluctuations, and Lender Portfolio Change

In this study we examine the effects of economic fluctuations on the repayment behavior of a portfolio of adjustable-rate mortgages (ARMs). Because the U.S. experience with ARMs is quite recent, we have used data on a form of ARM used in Canada, the rollover mortgage. The results of our analysis suggest that use of ARMs similar to the rollover mortgage may reduce but not eliminate interest-rate risk for lenders, as borrowers, albeit constrained, prepay above-market-rate loans. In addition, we find that the periodic payment change inherent in the rollover mortgage does not lead to higher default rates and, therefore, credit risk.     

PAYING FOR LOYALTY: PRODUCT BUNDLING IN OLIGOPOLY*

In recent times, pairs of retailers such as supermarket and retail gasoline chains have offered bundled discounts to customers who buy their respective product brands. These discounts are a fixed amount off the headline prices that allied brands continue to set independently. We show that a pair of firms can profit from offering a bundled discount to the detriment of other firms and consumers whose preferences are farther removed from the bundled brands. Indeed, when both pairs of firms negotiate bundling arrangements, there are no beneficiaries and consumers simply find themselves consuming a sub‐optimal brand mix.     

An antitrust analysis of bundled loyalty discounts

Consider a monopolist in one market that faces competition in a second market. Bundled loyalty discounts, in which customers receive a price break on the monopoly good in exchange for making all purchases from the monopolist, have ambiguous welfare effects. Such discounts should not always be treated as a form of predatory pricing. In some settings, they act as tie-in sales. Existing tests for whether such discounts violate competition laws do not track changes in consumer surplus or total surplus. We apply a new test to an illustrative example based on SmithKline that assumes the “tied” market has homogeneous goods. If the tied market is characterized by Hotelling competition, bundling by the monopolist causes the rival firm to reduce its price. In numerical examples, we find that this can deter entry or induce exit.     

Movers and Shuckers: Interdependent Prepayment Decisions

We model competing risks of mortgage termination where the borrower faces a repeated choice to continue to pay, refinance the loan, move or default. Most previous empirical work on mortgage prepayment has ignored the distinction between prepayments triggered by refinancing and moving, combining them into a single prepayment rate. We show that financial considerations are the primary drivers of the refinance choice while homeowner characteristics have more influence on the move decision. We demonstrate that these differences are statistically significant and that combining these two distinct choices into a single measure of prepayment shifts coefficients toward zero and produces inaccurate predictions of aggregate termination rates. For example, a combined model underestimates the effect of the market price of the loan on refinancing; it misses entirely the opposite effects of borrower income on moving and refinancing. Our results suggest that existing prepayment models are inconsistent predictors of mobility-driven prepayment and underestimate the effect of market conditions and borrower characteristics on refinancing and housing decisions. Our findings have great significance to mortgage investors because mobility-driven prepayments are likely to be a more significant source of prepayments in thenext decade.