[quanto]

Your intuition is quite correct. These methods (Leif et al) do not extend well to different boundary or intermediate conditions that are quite necessary in real life scenarios. AFAIK, there are a few teams on the Street that do fairly advanced numerical analysis, but most resort to Monte Carlo or some statistically-informed perturbation theory.

(I wish I could talk more, but yeah, legal obligations)

[fakesson]

Monte Carlo might be ok to OTC derivatives, however for automatic market making of exchange traded option, which are mostly American, it would be too slow.

After a bit more googling, I found these more recent slides by Jesper Andersen, where he believes that the Leif et al method could be extended for local vol (see page 25): https://www.cqfinstitute.org/sites/default/files/4%20-%20Jes...

[Agingcoder]

I go through academic literature on a regular basis, hoping that some kind of really major improvement might magically appear. Usually the ideas are great, but they don’t survive real life equities markets ( from dividends to non convex payoffs, local vol etc )