Pricing and Hedging of a Mortgage Portfolio

Abstract

Forecasting the prepayments is essential for any financial institution providing mortgages, and it is a crucial step in the hedging of the risk resulting from these unexpected cash flows. The way in which the prepayment rate is predicted impacts on the hedging strategy. For example, if the prepayment model is deterministic only the average prepayments are forecast, and a linear hedge composed of swaps is sufficient. However, in condition of volatile markets the lack of a non-linear hedge can result in losses for the bank. Considering that the there is a correlation between the prepayments and the level of interest rates in the market, we propose a prepayment model which is only based on the refinancing incentive. This way, the prepayments' forecast might be less accurate, but the clear link with the market allows to extend the prepayment model to a stochastic environment. We showed that allowing the notional of a mortgage to be stochastic unveils the non-linear risk embedded in the prepayment option, arising the necessity to include non-linear instruments in the hedging portfolio. The calibration of the refinancing incentive on a data set of more than thirty millions of observations led us to choose the functional form of the prepayments that is able to capture the borrowers' behaviour the most, and it distinguishes the model from full-rational models in which the option to prepay is assumed to be always exercised rationally. Then, the linear and non-linear risks are addressed to a set of tradeable instruments, aiming to build a static hedge. Different combinations of swaps and swaptions are tested, in order to determine which derivatives have the highest replication power. This research can impact considerably the evaluation of the exposure to interest rate risk of mortgage providers, and it can improve the performance of the hedging of the prepayment risk. Moreover, since the linear and non-linear components of the risk embedded in mortgages are distinguished, it can also help in the pricing of the prepayment option, allowing banks to define the mortgage rates with more accuracy.