A direct LU solver for pricing American bond options under Hull–White model

The main goal of this paper is to propose a novel numerical algorithm to price American options on bonds. For this purpose, we illustrate the performance of this method by means of the valuation of an American Put Option on a discount bond under the extended Vasicek model due to Hull and White (HW) and using the consistent forward rate curves. In particular, an implicit Crank–Nicolson (CN) scheme in time is applied obtaining a discretized linear complementarity problem (LCP) and then we introduce a direct LU based method to solve the LCP. Finally, we carry out numerical experiments to examine the convergence of this method and to testify the efficiency and effectiveness of this numerical scheme against other standard approaches.