A Spectral Method for Bonds

We present an spectral numerical method for the numerical valuation of bonds with embedded options. We use a CIR model for the short term interest rate. The method is based in a Galerkin formulation of the relevant partial differential equation for the value of the bond discretized by means of orthogonal Laguerre polynomials. The method is proved to be very efficient, it shows a high precision for the type of problem we treat here and it is easy to use with more general models with non constant coefficients. As a consequence it can be a possible alternative to other approaches employed in practice specially when it is needed a calibration of the parameters of the model to match the observed market data.