Pricing and Hedging Prepayment Risk in a Mortgage Portfolio

TL;DR

This paper develops a stochastic model for mortgage prepayment risk, incorporating non-linear financial instruments into hedging strategies, calibrated with extensive data to accurately reflect borrower behavior and improve risk management.

Contribution

It introduces a new model capturing non-linear prepayment risks and proposes a static hedge strategy using both linear and non-linear instruments, calibrated with large-scale data.

Findings

The model accurately reflects borrower prepayment behavior.

Inclusion of non-linear instruments improves hedging effectiveness.

Calibration with 30 million observations validates the model's accuracy.

Abstract

Understanding mortgage prepayment is crucial for any financial institution providing mortgages, and it is important for hedging the risk resulting from such unexpected cash flows. Here, in the setting of a Dutch mortgage provider, we propose to include non-linear financial instruments in the hedge portfolio when dealing with mortgages with the option to prepay part of the notional early. Based on the assumption that there is a correlation between prepayment and the interest rates in the market, a model is proposed which is based on a specific refinancing incentive. The linear and non-linear risks are addressed by a set of tradeable instruments in a static hedge strategy. We will show that a stochastic model for the notional of a mortgage unveils non-linear risk embedded in a prepayment option. Based on a calibration of the refinancing incentive on a data set of more than thirty million observations, a functional form of the prepayments is defined, which accurately reflects the borrowers' behaviour. We compare this functional form with a fully rational model, where the option to prepay is assumed to be exercised rationally.