QuoteOriginally posted by: cosmologistQuoteOriginally posted by: CuchulainnThe lack of smoothness is payoff influences accuracy.Take a cash-or-nothing futures put S = 100, K = 80, Q (G) = 10, T = 0.75, r = 0.06, q = r, s = 0.35; P = 2.6710.Stress NT = 500. Tian P = 6.85896. CRR P = 2.20454Tian with Thomee?Wahlbin (Heston/Zhao) with simple Trapezoid averaging P = 2.66888.Dear Daniel,Are you stating that for the given case, the Put values can be either of 6.85896 or 2.20454?May be I am interpreting your results wrongly. Could you please explain? Thanks in advance.SidHi Cosmo,Nice to see you again.I tested 3 methods indeed, 2 of which are off the mark. A major issue is that discontinuous payoff has adverse effects on accuracy. This is well-known in PDE and Thomee/Wahlbin used averaging in 1974. Heston and Zhou do the same for lattices and have useful hints but their paper does not seem to be well-known.I tested a cash-or-nothing (~ scary Heaviside function). So, I tried maligned CRR which was better than 'straight' Tian (which never converges it seems). Now I took a simple (trapezoid) averaging and I got the improvements that you see.Stefanie Mueller uses Richardson extrapolation which may reduce computation time. I cannot give a definite conclusion (yet) on RE. Convergence is a bit erratic.I have not yet done averaging on plain options by averaging around the strike. hthDON THE RATE OF CONVERGENCE OF DISCRETE-TIME. CONTINGENT CLAIMS. STEVE HESTON. Goldman Sachs & Co., New York. GUOFU ZHOU.
Last edited by Cuchulainn
on May 5th, 2015, 10:00 pm, edited 1 time in total.