2 ms·
Crank-Nicolson is probably the least objectionable part of the method, but I prefer ADE. There are two numerically painful parts of the problem: the advection
by scott00 3y ago
Crank-Nicolson is probably the least objectionable part of the method, but I prefer ADE.
There are two numerically painful parts of the problem: the advection term and the oscillation inducing terminal condition (because it has a discontiuous derivative). I like to deal with advection by transforming the equation to an advection free equation. I'm under NDA on the best solution to the oscillatory terminal condition so I can't give that one away unfortunately.
- quanto 3y agoIndeed, a transformation (of some kind) is fairly standard, including the derivation for the standard analytic solution for European options. AFAIK, discontinuous first derivative per se may act as a seed to an oscillation due to its high frequency content that are not captured by any finite resolution algorithm (n.b. Gibbs phenomenon). But it is Crank-Nicolson that characteristically creates these oscillatory problems -- in other words, there are algorithms that can gracefully handle the discontinuity without creating oscillation.
- scott00 3y agoYeah, the discretization interacts with the oscillation for sure. Full implicit is better than CN with regards to oscillation for instance, but I don't think would be a net win. Running a few implicit steps before switching to CN might help, though I've never tried it.