Prepayment modelling: a stochastic PSA approach with application to RMBS pricing

Details

Supervisors

Vrins, Frédéric

Faculty

Louvain School of Management

Degree label

Master [120] en ingénieur de gestion

Abstract

Prepayment modelling has been subject to extensive studies and numerous models have seen since then seen the light of day. Despite there being a large spectrum of models available, ranging in both complexity and efficiency, the deterministic prepayment model from the Public Securities Association (PSA) remains a common choice among practitioners. This thesis presents a stochastic approach to the PSA model in context of fully amortizing RMBS with a fixed coupon rate and guaranteed by a government agency. Annual prepayment rates maintain their simplistic aging structure and are defined as h(t) = 0.06 min(1, t / 30) X, where X defines a multiple of the PSA benchmark, but is now a random variable. An initial multiple X (at t=0) is determined as to represent turnover-related prepayment, after which X will evolve according a CIR process with an added drift term. The latter accounts for refinancing incentive created by sufficiently low levels of interest rates and ultimately embeds the PSA model with interest rate dependency. A case study is analyzed where the model is applied to two different types of RMBS, a Pass-Through and a Collateralized Mortgage Obligation (CMO). We analyze how the resulting prepayment rates behave in different interest rate scenarios and highlight the respective implications it has on the valuation of the aforementioned securities. A sensitivity analysis of the various parameters is also presented. We note that all computations are made using RStudio, an environment for statistical computing and graphics exploiting the programming language R.