Pricing european options on zero-coupon bonds with a fitted finite volume method

We present a novel numerical scheme to price European options on discount bond, where the single factor models are adopted for the short interest rate. This method is based on a fitted finite volume (FFVM) scheme for the spatial discretization and an implicit scheme for the time discretization. We show that this scheme is consistent, stable and monotone, hence it ensures the convergence to the solution of continuous problem. Numerical experiments are performed to verify the effectiveness and usefulness of this new method.