Academic journal article Real Estate Economics

Innovations in Mortgage Modeling: An Introduction

Academic journal article Real Estate Economics

Innovations in Mortgage Modeling: An Introduction

Article excerpt

This special issue presents a selection of recent methodological advances in the academic literature on mortgage performance and valuation. The articles include a range of modeling techniques from rational structural models applied to pool-level data and loan-level reduced-form, or behavioral, models of prepayment and default. Both classes of model are shown to be effective for evaluating innovations in contracting such as defeasance options in commercial mortgage contracts and hybrid residential mortgage products. Finally, the articles highlight a number of important methodological linkages between recent advances in mortgage modeling and those found in the valuation of other forms of risky debt such as corporate bonds.

The structural models presented here focus on pricing and modeling credit or call events that are specific to a particular class of borrower. These models focus on the underlying dynamics of interest rates and the assets that are the collateral on the mortgage. Credit (or call) events are triggered by random movements in the asset price relative to a threshold that is the exercise price on the option. By modeling credit or call events in terms of the underlying dynamics of asset prices and/or interest rates, the structural methodology functionally links option exercise events to the underlying fundamentals faced by the borrower. These articles build upon an extensive literature with a corporate debt focus: Leland (1994), Jarrow and Turnbull (1995), Longstaff and Schwartz (1995), Leland and Toft (1996), Anderson and Sundaresan (2000), Collin-Dufresne and Goldstein (2001) and Huang and Huang (2002), among many others. They also build upon important prior structural mortgage models including Dunn and McConnell (1981a,b), Timmis (1985), Johnston and van Drunen (1988), Kau et al. (1992), Stanton (1995), Kau et al. (1995) and Kau and Slawson (2002), among many others.

In contrast, reduced-form, or behavioral, approaches, do not explicitly model the value of the borrower's assets and capital structure. Instead credit and/or call events are modeled as exogenously specified jump processes or hazard rates. These approaches emphasize empirical estimation of the random timing of option exercise events. Bond valuation requires computing conditional expectations under a risk-neutral probability of functionals of event timing and realized cash flows. Recent examples of the reduced-form approaches to the valuation of corporate risky debt include Jarrow and Turnbull (1995), Duffee (1998), Duffie and Singleton (1999), Collin-Dufresne and Solnik (2001) and Duffie and Lando (2001). Schwartz and Torous (1989) develop one of the first reduced-form mortgage-backed securities (MBS) valuation models in which prepayment was modeled as a function of a set of (nonmodel based) explanatory variables. Deng, Quigley and van Order (2000) developed a sophisticated competing risk reduced-form model of mortgage termination performance using loan-level data.

In many ways, the characteristics of mortgages and MBS make these instruments particularly suitable for developing and testing reduced-form models and multifactor structural valuation models. One advantage of mortgages over many other forms of defaultable and callable debt is that there are very extensive time series available on the prepayment and default experience of these bonds. In addition, the structure of mortgages and MBS is relatively simple. For mortgages, there is usually only one property that serves as collateral for the loan. For pass-through MBS, there is only one type of bond, so issues related to the seniority of the bonds do not apply. This stands in contrast to many other structured finance vehicles, such as collateralized debt obligations, which typically have complicated seniority structures, or corporate bonds, whose values depend upon the entire capital structure of the firm. Finally, when mortgage defaults are triggered for agency-insured MBS, such as Freddie Mac Participation Certificates or Ginnie Mae MBS, the principal recovery rates are 100%. …

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