A numerical method for pricing spread options on LIBOR rates with a PDE model

In this paper we present a new numerical method for solving a Black–Scholes type of model for pricing a class of interest rate derivatives: spread options on LIBOR rates. The interest rates are assumed to follow the recently introduced LIBOR Market Model. The Feynman–Kac theorem provides a PDE model for the spread option pricing problem which is initially posed in an unbounded domain. After a localization procedure and the consideration of appropriate boundary conditions in a bounded domain, we propose a Crank–Nicholson characteristic time discretization scheme combined with a Lagrange piecewise quadratic finite element for the spatial discretization. In order to illustrate the performance of the PDE model and the numerical methods, we present a real example of spread option pricing.