QuoteOriginally posted by: CuchulainnQuoteFor 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 withvolatility of volatility ~ O(1) and also small (not sure which is the more difficult for pde'sFor 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.Do you get these problems with NDSolve as well as Leisen method? My feeling is that rho is not a show-stopper in general. What are effects of applying 'wrong' but 'easy' BCs on accuracy?If we take the non-Feller case - thus allowing Dirichlet BC - then all I would need is the BC for a call (put)1. S = 0, S = 11. v = 0, v = 1//and input data as well would be nice as well.BTW there are 3 interpretations of Heston which result in different input parameters.OK, I just tried my (hybrid) generic pde solver that handles what I call the SV(p) model:dV = (a - b V) dt + c V^p dW, taking p=(1/2)=Heston and a = b = c = V0 = T =1 and S0 = K = 100, Cost of carry parameters=0Also the number of spatial points was 100.This is really a cheat for your question because my hybrid method solves a pde in 1 spatial dimension andthen does the Fourier integration. But, you may find the test values useful. Call=Put values for various rho: rho pde(hybrid) `exact'-----------------------------0.0 37.3996 37.3994-0.1 37.0937 37.0934-0.2 36.7926 36.7924-0.3 36.4958 36.4957-0.4 36.2030 36.2028-0.5 35.9137 35.9135-0.6 35.6277 35.6275-0.7 35.3449 35.3446-0.8 35.0651 35.0649-0.9 34.7888 34.7884-1.0 34.5166 34.5158So, at least by this hybrid method, extreme rho is no problem for NDSolve.If you apply the wrong boundary conditions and the boundary is hittable, you'll get convergence tothe wrong solution. If the boundary is not hittable, interior values (but not the boundary value) can converge tothe correct solution, but it is not a clean approach, IMO.What are the 3 interpretations of Heston?
Last edited by Alan
on February 17th, 2012, 11:00 pm, edited 1 time in total.