If I am not in error, the far-field BC on vol is external. What is a "characteristic boundary" in this context?Unit-transformation is sexy but I get oscillations in the solution due to the (1-sigma) as denominator, when sigma -> 1 (I tested various implementations in the domain range of the products in am working with) I think this is a numerical issue that does not affect only vol=1, so a (1-sigma-epsilon) adjustment at vol=1 is not fixing this on my side.The oscillations I get are quite an expensive price to pay for the luxury of avoiding domain truncation, in my view.Furthermore, in my trading activity, the "interesting box" is in the neighborhood of the strike price: Unit-transformation forces me to spend time to calculate grid points for very high vols and prices. In order to get a higher resolution in the "interesting box", a non-uniform-mesh could be used, but that increases the complexity and the computational efforts.The results I am most happy with are:-> ADE (40% faster than ADI)-> Standard SABR, which is numerically more solid-> Heston BCs where I've found a nice trade-off between the point of truncation and how much of "a good approximation" of the solution the far-field BCs are... but there's lot of research to be done on this topic.[Edited: .. I've tried to improve my english]
Last edited by chocolatemoney
on October 10th, 2012, 10:00 pm, edited 1 time in total.