Short Rate Models: Hull-White or Black-Karasinski? Implementation Note and Model Comparison for ALM

Abstract

In this paper, we compare two one-factor short rate models: the Hull White model and the Black-Karasinski model. Despite their inherent shortcomings the short rate models are being used quite extensively by the practitioners for risk-management purposes. The research, as part of students' projects in collaboration with the Asset-Liability-Management (ALM) Group of ABN AMRO Bank, provides detail procedures on the implementation, and assesses model performance from an ALM perspective. In particular, we compare the two models for pricing and hedging Bermudan swaptions because of its resemblance to prepayment option in typical mortgage loans. To our knowledge, the implementation of the two short rate models (and the Black-Karasinski model in particular) is not well documented. We implemented the two models using interest rate derivatives on Euro and US rates over the period February 2005 to September 2007 and with the Hull-White trinomial tree. Our results show that in terms of the in-sample pricing tests, the one-factor Hull-White model outperforms the Black-Karasinski model. The estimated parameters of Hull-White model are also more stable than those of the Black-Karasinski model. On the other hand, the tests for the hedging performance show that the Black-Karasinski model is more effective in hedging the interest rate risk of the at-the-money 10x1 co-terminal Bermudan swaption.