The General Hull-White Model and Super Calibration

Abstract

Term structure models are widely used to price interest-rate derivatives such as swaps and bonds with embedded options. This paper describes how a general one-factor model of the short-rate can be implemented as a recombining trinomial tree and calibrated to market prices of actively traded instruments such as caps and swap options. The general model encompasses most popular one-factor Markov models as special cases. The implementation and the calibration procedures are sufficiently general that they can select the functional form of the model that best fits the market prices. This allows the model to fit the prices of in- and out-ofthe- money options when there is a volatility skew. It also allows the model to work well very low interest-rate economies such as Japan where other models often fail.