Pricing default risk in mortgage-backed securities under a regime-switching reduced-form model

Abstract

In this paper, we propose a reduced-form model to price default risk in mortgages and fixed-rate pass-through mortgage-backed securities. Since the default of borrowers is often affected by macroeconomic conditions, we take into account the changes of market regimes. We introduce a default factor process to model the default risk of borrowers and define its exponential decreasing rate as default rate, which follows a shot-noise process. The model assumes that the interest rate and the default rate are all influenced by macroeconomic conditions described by a homogeneous Markov chain. Explicit pricing formulas for mortgage-backed securities with defaultable underlying mortgages are obtained through the conditional Laplace transform of the regime-switching shot-noise process. Numerical illustration is also presented to show the impact of model parameters on the price.