Anatomy of an ARM: The Interest-Rate Risk of Adjustable-Rate Mortgages

This article analyzes the dynamics of the commonly used indices for adjustable rate mortgages and systematically compares the effects of their time-series properties on the interest-rate sensitivity of adjustable-rate mortgages. Our ARM valuation methodology allows us simultaneously to capture the effects of index dynamics, discrete coupon adjustment, mortgage prepayment, and both lifetime and periodic caps and floors. We can, moreover, either calculate an optimal prepayment strategy for mortgage holders or use an empirical prepayment function. We find that the different dynamics of the major ARM indices lead to significant variation in the interest-rate sensitivities of loans based on different indices. We also find that changing assumptions about contract features, such as loan caps and coupon reset frequency, has a significant, and in some cases unexpected, impact on our results.     

Valuing Mortgage Insurance Contracts in Emerging Market Economies

We develop a new option-based method for the valuation of mortgage insurance contracts in closed form in an economy where agents are risk neutral. While the proposed valuation method is general and can be used in any market, it may be particularly useful in emerging market economies where other existing methods may be either inappropriate or are too difficult to implement because of the lack of relevant data. As an application, we price a typical Serbian government-backed mortgage insurance contract.     

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.     

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.     

Credit Risk and the Term Structure of Lease Rates: A Reduced Form Approach

Previous research either assumes default free leases or leases subject to default risk using a structural approach. However, structural credit risk models suffer from a common criticism that the firm’s asset value process is unobservable. We develop a reduced form credit risk model for leases that avoids making assumptions regarding unobservable asset valuation processes. Furthermore, we assume a correlated market and credit risk that provides us with a simple analytic formula for valuing defaultable lease contracts. Numerical analysis reveals that tenant credit risk can have a substantial impact on the term structure of leases. Finally, we use the model to demonstrate the implied lease term structure for a set of retail and financial firms in the Fall of 2000.

The prepayment option on mortgage securities: A random coefficient approach

Using the Swamy (1970) model for pooled data and a Hildreth and Houck (1968) model for individual securities, this article investigates whether the parameters describing the prepayment behavior of the fixed-rate debt underlying mortgage-backed securities are better estimated as a stochastic behavior. Empirical results indicate that differences between securities are random. The Hildreth and Houck model yields additional information on randomness over time. The use of the aggregate data to estimate prepayment of individual securities, as opposed to use of the prepayment history of the individual security, may yield more reliable results.     

Reduced Form Mortgage Pricing as an Alternative to Option-Pricing Models

This paper extends the traditional hazard technique of estimating prepayment and default by allowing their baselines to be stochastic processes, rather than known paths of time, as is typically assumed. By working in the reduced form, this method offers an alternative to the empirical valuation of mortgages more easily implemented than the standard structural form approach of options pricing.     

A Semiparametric Method for Valuing Residential Locations: Application to Automated Valuation

This paper is motivated by automated valuation systems, which would benefit from an ability to estimate spatial variation in location value. It develops theory for the local regression model (LRM), a semiparametric approach to estimating a location value surface. There are two parts to the LRM: (1) an ordinary least square (OLS) model to hold constant for interior square footage, land area, bathrooms, and other structural characteristics; and (2) a non-parametric smoother (local polynomial regression, LPR) which calculates location value as a function of latitude and longitude. Several methods are used to consistently estimate both parts of the model. The LRM was fit to geocoded hedonic sales data for six towns in the suburbs of Boston, MA. The estimates yield substantial, significant and plausible spatial patterns in location values. Using the LRM as an exploratory tool, local peaks and valleys in location value identified by the model are close to points identified by the tax assessor, and they are shown to add to the explanatory power of an OLS model. Out-of-sample MSE shows that the LRM with a first-degree polynomial (local linear smoothing) is somewhat better than polynomials of degree zero or degree two. Future applications might use degree zero (the well-known NW estimator) because this is available in popular commercial software. The optimized LRM reduces MSE from the OLS model by between 5 percent and 11 percent while adding information on statistically significant variations in location value.     

Optimal Mortgage Refinancing: A Closed‐Form Solution

We derive the first closed‐form optimal refinancing rule: refinance when the current mortgage interest rate falls below the original rate by at least In this formula W(.) is (the principal branch of) the Lambert W‐function, where 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, 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.     

A Prepayment Model for the Japanese Mortgage Loan Market: Prepayment-Type-Specific Parametric Model Approach

This paper proposes a framework for construction of a prepayment model suitedto the Japanese mortgage loan market and assesses the validity of thisframework based on an empirical analysis using data from Japan. In thisframework, a model is constructed for each of three prepayment types, namely,`full prepayment', `partial prepayment', and `subrogation', using a parametricproportional hazards model, which was also employed by Schwartz and Torous(1989). Combining these three types of models allows one to take into accountthe effects of partial prepayments, which are frequently used in the Japanesemortgage market, and to simultaneously construct a model for both prepaymentand default. Time-dependent (path-dependent) covariates are introduced intothe model, which are estimated by the maximum likelihood method based on thefull likelihood that takes into account the time-dependence of the covariates.Results of the empirical analysis indicate that the hazard functions differsubstantially depending on the prepayment type. In addition, results indicatethat the fit of the model can be improved by the distinction of prepaymenttypes and the introduction of the market interest rates as path-dependentcovariates.     

A Reduced‐Form Model for Warrant Valuation

This paper studies warrant valuation using a reduced‐form model. Analogous to the credit risk literature, structural models require complete information about the asset value process and the firm’s liabilities. In contrast, reduced‐form models require only information about the firm’s stock price process. We introduce a reduced‐form model where the warrant holder is a price taker, and we relate our model to structural models appearing in the literature.     

Exploring Formula Allocation for the European Union

This paper explores the efficiency impacts of two methods of consolidated base taxation with formula allocation under consideration in the European Union. The first method, common (consolidated) base taxation (CCBT), would allow companies to choose a single tax base for their EU-wide operations. This tax base would be common throughout the participating member states. The second method, Home State taxation (HST), would also allow companies to choose a single tax base for their EU-wide operations. But, unlike with CCBT, the tax base would be defined according to the rules in the company's residence, or home, state. Thus, several different tax bases would exist within the EU. Both methods would use a common formula to distribute profits across countries. This paper finds that since countries continue to set corporate income tax rates, economic inefficiencies continue to exist under both methods. However, under HST, since the tax base differs according to residence, additional inefficiencies may arise depending on whether countries reduced their tax rates to combat the incentive for companies to relocate to locations with narrow tax bases.     

内资企业组织形式的纳税筹划

在现行税制下,内资企业由于组织形式的不同,会适用不同的所得税,即个人所得税或企业所得税。由于这两种所得在税率上和费用扣除方面存在差异,纳税人可以利用这些差异进行纳税筹划。     

A Bayesian framework for combining valuation estimates

Discounted cash flow, method of comparables, and fundamental analysis typically yield discrepant valuation estimates. Moreover, the valuation estimates typically disagree with market price. Can one form a superior valuation estimate by averaging over the individual estimates, including market price? This article suggests a Bayesian framework for combining two or more estimates into a superior valuation estimate. The framework justifies the common practice of averaging over several estimates to arrive at a final point estimate.     

The Revenue Consequences of Using Formula Apportionment to Calculate U.S. and Foreign-Source Income: A Firm-Level Analysis

This paper examines the 1989–1993 publicly available financial reports of 46 U.S.-based multinationals to estimate the revenue implications of implementing a U.S. federal formula apportionment system. Ignoring behavioral responses, we estimate shifting to an equal-weighted, three-factor formula would have increased their U.S. tax liabilities by 38 percent, with an 81 percent increase for oil and gas firms. We find the firms report a lower percentage of their worldwide profits as American profits than their American share of assets, sales, or payroll. The results may be attributed to more profitable foreign operations, tax-motivated income shifting, or measurement error.     

A structural framework for modelling contingent capital

This paper develops a structural model of contingent capital. In contrast to existing approaches we explicitly link the firm’s total payout to its cost of debt, leading to a total payout that is linear in—as opposed to proportional to—asset value. In the special case that asset value evolves as affine geometric Brownian motion we derive closed-form expressions for limiting (i.e. perpetual) bond values. The proposed model is flexible, so that it can be used to gauge the relative merits of different variations of contingent capital, and parsimonious, so that it is relatively easy to implement in practice. An empirical example using data from the Canadian banking sector is provided that illustrates how the model can generate insights into problems that are of interest to both regulators and issuers of contingent capital (e.g. what range of conversion prices would be consistent with regulatory guidelines, and how expensive is contingent debt over this range).     

A Simple Induction Approach and an Efficient Trinomial Lattice for Multi-State Variable Interest Rate Derivatives Models

This paper presents an alternative approach for interest rate lattice construction in the Ritchken and Sankarasubramanian (1995) framework. The proposed method applies a parsimonious induction technique to represent the distribution of auxiliary state variables and value interest rate derivatives. In contrast to other approaches, this technique requires no numerical interpolations, approximations and iterative procedures for pricing interest rate options using a simple backward induction and, therefore, provides significant computational advantages and flexibility with respect to existing implementations. Also, the proposed trinomial interest rate lattice specification provides for a further reduction in computational costs with additional flexibility. The results of this work can be extended to a class of derivatives pricing models with path dependent state variables and generalized to multi-factor models.     

A comprehensive structural model for defaultable fixed-income bonds

An exact valuation formula for defaultable corporate coupon bonds is proved. The model incorporates discrete coupons, bankruptcy costs, taxes and the market risk generated by a stochastic risk-free structure. The aim of this paper is twofold: first, we generalise previous pricing models for corporate bonds; second, we provide a comprehensive formula in order to properly disentangle the contribution of several risk factors to credit spreads.