Analyse temporelle du risque de prépaiement : le cas de Belfius

Abstract

Over the last years, the mortgage rates have greatly evolved. Therefore, sensitive borrowers will prepay their mortgage loan when interest rates fall to a particular level. However, some borrowers will never prepay their loan or will do it even if interest rates increase sometimes for personal reasons such as divorce, death or house moving. Consequently, the aim of this dissertation is to evaluate the impact of parameters on the probability of prepayments. This master thesis presents the development of a prepayment model for mortgage loans. In order to make the computations, we do not use a sample but the whole database of Belfius concerning fixed rate mortgage (FRM) between January 2005 and December 2017. To implement this model, a quarterly time set has been adopted. The probability of prepayment is modelled thanks to a logit procedure, which consists of a binary choice model: prepaid (=1) or not prepaid (=0). The best model up to now implemented by Belfius including 4 parameters has been used as a starting point. According to the literature, the constant prepayment rate (CPR) increases with the mortgage loan age. This is called the seasoning effect where a S-shaped prepayment function between mortgage age and prepayments appears. Prepayments apparently seems to be seasonally dependent meaning that prepayments increase during the summer months and decrease during the winter months. Our goal is to test these two concepts related to time. The main results of the empirical research showed that, all other things being equal, conditional prepayment rates of FRM are generally low in the first years of a mortgage. Then, it increases as the age of the mortgage rises and diminishes for the last years. However, FRM prepayments are seasonally independent. Based on Belfius credits, no seasonal trend can be identified. Rates fluctuations remain the most significant element in a prepayment decision. Actually, this rate change is incorporated in the calculation of the client gain.