A front-fixing method for American option pricing on zero-coupon bond under the Hull and White model

Abstract

ABSTRACT: A new efficient numerical method is proposed for valuation of American option on zero-coupon bond using Hull and White model. By applying the front-fixing transformation suggested by Holmes and Yang, the original free boundary problem is transformed into a new fixed boundary partial differential equation (PDE) problem, where the optimal stopping boundary is one of the unknowns of the problem. The numerical finite difference scheme for the transformed problem is constructed. Stability and convergence rate is studied empirically. Numerical simulation of the computation of both the option price and the optimal stopping boundary are illustrated with examples and the comparison with the Hull and White tree method.