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QuoteOriginally posted by: Cuchulainntrias,Just to get me back on track, what is the status of the problem at this time? Does the non-jump case produce efficient results?Yes and no. It does not produce efficient results on its own. But adding some control variate techniques helps a lot. But it's still not perfect. However, for some reason, pricing VG American calls with a small grid (50x100) gives perfect results. So it looks like just the American puts have trouble.Also, after some math analysis, I concluded that you cannot integrate over American BS prices to come up with an American VG price.

As a possible Plan B you might wish to look at this nice article which is a rigorous approach (viscosity) to PIDE for Levy processes. It uses a IMEX scheme and maybe you can use their approach for the integral part (they truncate the integral and use the trapezoidal rule). Certainly worth a look. If your code is modular then you should replace the integral stuff.Cont, Rama and Voltchkova, Ekaterina "A finite difference scheme for option pricing in jump diffusion and exponential Levy models" SIAM J. Num. Analysis 43(2005), pp. 1596-1626.

QuoteOriginally posted by: trias10Also, after some math analysis, I concluded that you cannot integrate over American BS prices to come up with an American VG price.this is pretty obvious, the exercise boundary will depend on the model

Pricing of Barriers for example by PIDE for VG and its applications to CDS pricing can be found in our paper http://www.schoutens.be/cds.pdf ; The algorithm can easily be adapted to pricing of other types of options, like bermudian, american, digitals etc