Efficient calibration of the Hull White model

Abstract

SUMMARY In this paper we study the calibration of the Hull White interest rate model for the pricing of Bermudan swaptions and Bermudan bond options. A common modelling approach for the calibration of the Hull White model is to choose the model parameters such that market prices of corresponding European derivatives are replicated by the model. This requires that a multidimensional non-linear optimization problem has to be solved. The focus of this paper lies in the efficient formulation and numerical solution of this optimization problem. We investigate the numerical properties of the iterative solution of the optimization problem by means of a Gauss Newton and an Adjoint Broyden quasi-Newton method. Required derivatives of the objective function are evaluated by techniques of Automatic Differentiation. The algorithms are benchmarked to Minpack's general purpose solver HYBRD. Numerical results for the calibration of long-term Bermudan swaptions are reported. Copyright © 2011 John Wiley & Sons, Ltd.