QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: rmaxWhy do you get the saw tooth profile?1. I took NX = NY = NT = 300 which is very conservative.2. Took absolute value of FD solution vs Margrabe solution.3. Almost perfect correlation, mixed derivatives may dominate. It is a stress test that kills many schemes.4. Payoff has a discontinuity on S1 = S2, has not been smoothed.Having said that, Janenko scheme gives max error 0.009. BTW many examples/articles take rho in the safe zone [-0.5, 0.5] Now, my new 2 posts take NX = 300 = NY with various NT (500, 700, 100). At some stage increasiing NT has no effect and then we can set NX = NY = 400 etc.As I mentiiond, Excel is not optimal, e.g. cannot create other graph from 400X400 matrix. Saw OpeVRML C++ boost library.For SV models, large |rho| is also a difficult numerical regime. When you get to it, will be interesting tosee your error plots for, say, Heston model with rho in (-1,-0.9) combined with volatility of volatility ~ O(1) and also small (not sure which is the more difficult for pde's For example, my OptionCity calculator uses the Leisen lattice algorithm and this has a specific limitation: |rho| < Sqrt[3/4]I'll have to see how Mathematica's NDSolve does for some extreme rho.
Last edited by Alan
on February 14th, 2012, 11:00 pm, edited 1 time in total.