Finite Difference Methods for Hull-White Pricing of Interest Rate Derivatives with Dynamical Consistent Curves

We study a novel implementation of the explicit and the implicit Crank-Nicolson (CN) numerical schemes for solving time-dependent Parabolic Partial Differential Equations (PDEs) in one spatial dimension in a variety of applications in computational finance related with the the One-Factor Hull-White Model. Finite differences on uniform grids are used for both the spatial and time discretization of the Hull-White PDE. Both implementations allow the use of dynamical Consistent Forward Rate Curves in Björk sense among others, as the traditional use of the Forward Induction technique is avoided. As examples, we apply these methods to price European and American-style Bond Options, European-style Interest-Rate Caps as well as Digital Caps with no early provision. Numerical results comparing the efficiency of these numerical implementations are provided