Valuation of Residential Mortgage-Backed Securities with Proportional Hazard Model: Cumulant Expansion Approach to Pricing RMBS

Abstract

This paper proposes a pricing formula for residential mortgage-backed securities (RMBS) with the proportional hazard model. First, we develop basic models of mortgage contracts with prepayment risk in the intensity-based framework. Next, assuming the proportional hazard model to describe prepayment risk, which is used as a typical prepayment model both academically and in practice; a general pricing formula for not only RMBS, but also IO and PO is derived by using the cumulant expansion method. Furthermore, it is also shown that the formula is applicable to various types of the proportional hazard models. Finally, numerical examples based on Japanese RMBS market data demonstrate that the formula is very accurate and useful in practice.