The numerical treatment of partial differential equations in computational finance started with binomial and trinomial trees, with all the drawbacks related to these approaches. In the meanwhile (see, e.g., Duffy 2004, in the July issue of this magazine), finite differences are widely used in modern derivatives pricing. We present how pricing software can be developed on the basis of finite element techniques, which allow more flexibility than finite differences.

Mean reverting models for interest rates tend to become numerically difficult in regions sufficiently far away from the mean-reverting level. The reason is that the convection dominates the diffusion in these regions, and therefore techniques for convection-dominated flows should be applied. We present how streamline diffusion is applied to obtain stable numerical schemes.

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