A Closed-Form Pricing Formula for Mortgages Incorporating Termination Hazard Rates and Recovery Rate as Correlated Stochastic Processes with Jump Components

Abstract

Before subprime, the major risk in a home mortgage loan other than interest rate risk was prepayment. Partly idiosyncratic but driven by interest rates, prepayment is modeled as being a path-dependent function of the mortgage rate in the market. Valuation typically is done by Monte Carlo simulation, which is time consuming and has some difficulty in properly reflecting rare events. Unlike for mortgages, the main reason for most loans for an abrupt cessation of payments is default. While “structural” credit risk models treat default as a function of asset prices, in “reduced form” models it is more like a lightning strike, which might hit any loan at any time, with the probability of occurrence being dependent on exogenous factors. In this article, Chiang and Tsai develop a reduced-form type framework for valuing risky mortgages that incorporates stochastic prepayment, default, and recovery after default as correlated Poisson processes with intensities driven by the underlying interest rates and house prices. This structure leads to closed-form valuation with a major improvement in efficiency. An empirical implementation on mortgage data from 2001 to 2010 then provides coefficient estimates the authors use to explore the sensitivity of loan value to the model parameters.