Optimal Mortgage Refinancing with Inattention

The purpose of this paper is to develop a dynamic model of mortgage refinancing in a contingent claim framework that simultaneously solves for the borrower's optimal mortgage refinancing strategy, the value of the refinancing call option, the value of the mortgage liability to the borrower, and the market (lender) value of the fixed‐rate contract. We also calculate the minimum differential between the contract rate on the existing mortgage and the current interest rate that is required to trigger an optimal mortgage refinancing.

We derive the first closed-form optimal mortgage refinancing rule. The expression is derived by using the Lambert-W function to solve a tractable class of mortgage refinancing problems. We calibrate our solution and show that our quantitative results closely match those reported by researchers who use numerical methods.

Optimal Mortgage Refinancing with Inattention

We derive the first closed-form optimal refinancing rule: Refinance when the current mortgage interest rate falls below the original rate by at least [Formula: see text] In this formula W(.) is the Lambert W-function, [Formula: see text]ρ is the real discount rate, λ is the expected real rate of exogenous mortgage repayment, σ is the standard deviation of the mortgage rate, κ/M is the ratio of the tax-adjusted refinancing cost and the remaining mortgage value, and τ is the marginal tax rate. This expression is derived by solving a tractable class of refinancing problems. Our quantitative results closely match those reported by researchers using numerical methods.

We build a model of optimal fixed-rate mortgage refinancing with fixed costs and inattention and derive a new sufficient statistic that can be used to measure inattention frictions from simple moments of the rate gap distribution.In the model, borrowers pay attention to rates sporadically so they often fail to refinance even when it is profitable.When paying attention, borrowers optimally choose to refinance earlier than under a perfect attention benchmark.Our model can rationalize almost all errors of "omission" (refinancing too slowly) and a large fraction of the errors of "commission" (refinancing too quickly) previously documented in the data.

A model of rational mortgage refinancing is developed where the drift and volatility of interest rate process switch between two regimes. Because of the possibility of a regime shift, the optimal refinancing policy is characterized by the different threshold of interest differential for each regime. Numerical simulation demonstrates that the optimal refinancing threshold in each regime can be smaller or larger than the threshold under single-regime models. Finally, we evaluate the predictions of the model, based on the estimated parameters for a two-regime model to capture the evolution of the mortgage rates in the US. Our model can produce both late and early refinancing, which is consistent with the observed refinancing behavior.

We derive the first closed-form optimal refinancing rule for mortgages: Refinance when the current mortgage interest rate falls below the original mortgage interest rate by at least (1/ψ)[φ W(-exp(-φ))], where W(.) is the principal branch of the Lambert W-function, ψ=((√(2(ρ λ)))/σ), φ=1 ψ(ρ λ)((κ/M)/((1-τ))), ρ is the real discount rate (e.g. ρ= 0.05), λ is the expected real rate of exogenous mortgage repayment, including the effects of moving, principal repayment, and inflation (e.g. λ= 0.15), σ is the annual standard deviation of the mortgage rate (e.g. σ=0.0109), κ/M is the ratio of the refinancing cost and the remaining value of the mortgage (e.g. κ/M= $4,500/$250,000), and τ is the marginal tax rate (e.g. τ= 0.28). This expression is derived by solving a tractable class of stylized mortgage refinancing problems. Our quantitative results closely match those reported by other researchers using numerical methods.

Optimal Mortgage Refinancing with Inattention

Despite the enormous volume of refinancing activity in conventional residential mortgages, reaching record levels during recent years of historically low interest rates, the solution to the problem of how to time refinancing decisions optimally has remained elusive. It is recognized that the decision should depend, among other factors, on the ‘call’ options of the outstanding and the new mortgage. Determining the value of these options is a challenge in the absence of an observable optionless mortgage yield curve. We solve this by calibrating a benchmark interest rate process to the value of the new mortgage and then apply the notion of refinancing efficiency to the timing decision. In particular, risk-averse decision makers can use refinancing efficiency to measure how close to optimal a refinancing is. We analyse the sensitivity of the decision to interest rate volatility and also show how to incorporate homeowner-specific considerations, namely borrowing horizon and income taxes. While calibration and ...

Comment

Abstract. Let ρρ* be the maximum likelihood estimator (MLE) of the parameter ρ in the first‐order autoregressive process with normal errors. The problem of optimality in the sense of weighted squared error is considered rather than moments of asymptotic distributions. Many unbiased estimators can be constructed, but the two‐dimensional sufficient statistic is incomplete. It is shown that dEρ* ‐ ρ→ 0 uniformly in ρ, and that dE(ρ*)/dρ→ 1 for all |ρ| > 1. For |ρ| > 1, it is known that the asymptotic distribution of {I(ρ)}12(ρ* ‐ ρ), where I(ρ) is the Fisher information, is Cauchy. It follows that the Cramèr‐Rao inequality will not yield useful results for investigating the limit of exact efficiency of any asymptotically unbiased estimator, including the MLE. For all |ρ| < 1, ρ* is asymptotically optimal in the sense of minimizing expected weighted squared error. In addition, for |ρ| < 1, ρ* minimizes the variance asymptotically.

Multicollinearity and the Estimation of Low-Order Moments in Stable Lag Distributions

Rare {ital B} decays provide an opportunity to probe for new physics beyond the standard model. In this paper, we propose to measure the {tau} polarization in the inclusive decay {ital B}{r_arrow}{ital X}{sub {ital s}}{tau}{sup +}{tau}{sup {minus}} and discuss how it can be used, in conjunction with other observables, to completely determine the parameters of the flavor-changing low-energy effective Hamiltonian. Both the standard model and several new physics scenarios are examined. This process has a large enough branching fraction, {approximately}few{times}10{sup {minus}7}, such that sufficient statistics will eventually be provided by the {ital B} factories currently under construction. {copyright} {ital 1996 The American Physical Society.}

Understanding mortgage choice

Ordered random variables (ORVs) are of great importance in statistical science. These random variables are organized in increasing order called generalized order statistics (GOS). It has tremendous applications in engineering and science due to the inclusion of ordered random variables. This article addresses recursive moments of Rayleigh-Rayleigh distribution using order random variables. Such moments are applicable in studying the characteristics of random variables in increasing order such as time to failure of an electronic devices. The characterization result is also obtained by simple moments.