We apply the Pseudospectral method to two fundamental financial equations: the Black-Scholes equation and the Cox Ingersoil Ross model of the term structure of interest rates. The former is used to price a European Call Option and the latter to price a zero coupon bond. Chebyshev polynomials are used as the basis functions and Chebyshev collocation points for the space discretisation. The Crank-Nicolson scheme is used for the time differencing. We have developed a C++ program to solve general second order linear parabolic equations, A parallel quasi-minimal residual version of the Bi-Conjugate Gradient stabilised algorithm is applied to solve the linear system on the AP3000, a parallel computer. The regular space domain and the smooth solutions often encountered in finance suggest the suitability of using this higher order technique.