  A contour integral method recently proposed by Weideman [IMA J. Numer. Anal.,
to appear] for integrating semi-discrete advection-diffusion PDEs, is extended
for application to some of the important equations of mathematical finance.
Using estimates for the numerical range of the spatial operator, optimal
contour parameters are derived theoretically and tested numerically. Test
examples presented are the Black-Scholes PDE in one space dimension and the
Heston PDE in two dimensions. In the latter case efficiency is compared to ADI
splitting schemes for solving this problem. In the examples it is found that
the contour integral method is superior for the range of medium to high
accuracy requirements. Further improvements to the current implementation of
the contour integral method are suggested.
