Recombining Trees for One-Dimensional Forward Rate Models

Abstract:     
There exist two classes of interest rate models. Short rate models (HW, CIR, BDT), easy in pricing and tough in calibration and forward rate models (HJM, BGM), easy in calibration and tough in pricing. Parameters in short rate models have no natural interpretation in terms of market volatility but many options can be priced on recombining trees. We find particularly inconvenient the procedure of fitting the initial yield curve - necessary for many short rate models. Parameters of forward rate models (especially BGM) have direct link to market volatility but there exists a common prejudice that recombining trees cannot be applied to forward rate models. This paper is an attempt to construct a model allowing both recombining trees and "calibration without programming". We would like to call both presented models "simplest possible term structure models" - at least we do not know any simpler model.

Keywords: BGM model, HJM model, calibration, Bermudan swaptions, Brady bonds

Working Paper Series