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I am using the results in Osterlee as my benchmark.Sadly this only constitutes 4 cases but even here Hagan, 3DFDM, Truncated Euler and Unbiased do not seem to be in full agreement for all parameter sets.Its a bit of a cheicken and egg scenario that's why I am keen to benchmark my code against other implementations.

Some questions:1. Do you take put or call?2. Can you use the Shroder exact solution? Useful?3. I have a bunch of MC fd schemes for Heston that I can easily modify for SABR.

I take a call (you can always use put call parity to convert)I have not tried Shroder (can you point me to the paper?)Great well which ever scheme you are most confident in lets use that?

Hugh,I modified my Heston MC code to SABR in a few minutes work. Tested EE (explicit in S and v) and EI (the other 6 methods not yet). ForFutures price ( F ) 100.00Strik price ( X ) 100.00Time to maturity ( T ) 0.50 Risk-free rate ( r ) 0.00%ATM Vol 10.00%Beta 0.70VolVol 10.00%Correlation ( rho ) 0.00Value 2.820360 (WHOSE IS THIS??? DD)Black-76 equivalent vol 10.00%for EE , C = 0.709234EI , C = 0.711489both with NT = 1000. NSIM = 200000. Polar Marsaglia for RNG. NOW, if we set beta == 1 thenExtrap 2.82761PC 2.94213EE 2.81483EI 2.801Maybe that's reason for discrepancy?

For Chen & Oosterlee Set IV (T = 5 presume and max(F-K, 0)) /*K = 0.07; T = 5.0; alpha = 0.8; beta = 0.4; rho = -0.6; r = 0.0; IC_S = 0.07; IC_V = 0.4; */ IE C = 0.329824EE C = 0.05202 EE is wrong, very?

Value 2.820360 (WHOSE IS THIS??? DD)This is the result from the Hagan formula as found in Haug's book ( can send the spreadsheet if you like).Indeed you can check the Black 76 case using the link below and it comes it at 2.85 thus Hagan and Black agree ATM as it should be (I just assume regular 10% vol).http://www.cba.ua.edu/~rpascala/greeks2/GFOPMForm.phpIf you look at p127/8 of roelof's thesis he gets very similar answers to Hagan for these parameters.Using osterless's unbiased scheme for the above paramerters I get0.7112and with truncated euler=0.7255which broadly matches your results.Thus we now have 6 different models with 2 different resultsThis is what is confusing me.0.71 does seem a little low even for a vanilla 6 month ATM option with 10% vol and starting val 100?Surely these is some scaling factor which is missing?For parameter set IV in osterleeIt is your EE set which seems correct?EI seems incorrect?

Quote0.71 does seem a little low even for a vanilla 6 month ATM option with 10% vol and starting val 100?Surely these is some scaling factor which is missing?I tried Predictor Corrector for this set as well and I get 0.71.... similar to EE and EI. This is a big difference with 2.8.. Set IV C&O page 19 K = 0.07; T = 5.0; alpha = 0.8; beta = 0.4; rho = -0.6; r = 0.0; IC_S = 0.07; IC_V = 0.4; EE 0.05202EI 0.0329824PC 0.0598375

Its really confusing?T=0.5 and 0.1 vol with 0.1 vvol should be within the comfort zone for Hagan.+ as I said 0.71 does seem low for a 6 month 0% ATM option struck at 100?But it's not obvious to me how to reconcile the two sets of answers?I'm not even certain which answer to accept as correct? The unbiased scheme works pretty well for the parameter sets shown in the osterlee paper but it also gives 0.71(ish) for the parameter set we have been testing?It seems likely that the simulation based schemes and your FD schemes are "correct" as they agree with each other, but that some assumption used to build these models are different some how to Black, Hagan and indeed Roelof's FD scheme.

Set IV C&O page 19 K = 0.07; T = 5.0; alpha = 0.8; beta = 0.4; rho = -0.6; r = 0.0; IC_S = 0.07; IC_V = 0.4; EE 0.05202EI 0.0329824PC 0.0598375Extrapolation is 0.050502//Shroder ref in C&O article.

QuoteOriginally posted by: CuchulainnHugh,I modified my Heston MC code to SABR in a few minutes work. Tested EE (explicit in S and v) and EI (the other 6 methods not yet). ForFutures price ( F ) 100.00Strik price ( X ) 100.00Time to maturity ( T ) 0.50 Risk-free rate ( r ) 0.00%ATM Vol 10.00%Beta 0.70VolVol 10.00%Correlation ( rho ) 0.00Value 2.820360 (WHOSE IS THIS??? DD)Black-76 equivalent vol 10.00%for EE , C = 0.709234EI , C = 0.711489both with NT = 1000. NSIM = 200000. Polar Marsaglia for RNG. NOW, if we set beta == 1 thenExtrap 2.82761PC 2.94213EE 2.81483EI 2.801Maybe that's reason for discrepancy?

I have now put some finishing touches on ADE for SABR (using truncation at moment). The results seem to be in line wth my MC results. Will give updates later as I am a bit intercommunicado now.