Efficient Calibration of Trinomial Trees for One-Factor Short Rate Models

Abstract

In this paper we discuss the implementation of general one-factor short rate models with a trinomial tree. Taking the Hull-White model as a starting point, our contribution is threefold. First, we show how trees can be spanned using a set of general branching processes. Secondly, we improve Hull-White's procedure to calibrate the tree to bond prices by a much more efficient approach. This approach is applicable to a wide range of term structure models. Finally, we show how the tree can be adjusted to the volatility structure. The proposed approach leads to an efficient and exible construction method for trinomial trees, which can be easily implemented and calibrated to both prices and volatilities.