Does anyone have some experiences to share concerning the homogenization (averaging) of a time dependent volatility of variance parameter in a Heston-type stochastic volatility model?More concretely, I'm currently working on an implementation of the Piterbarg homogenization formulae and ran into some severe deviations when testing my code for the effective term volatility of variance (formula (6) in "Time to Smile", Risk Magazine, May 2005) against the exemplary numbers given in table A of the mentioned paper. I am not able to reproduce the data on the stated tenor structure {0.02, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0} with a constant sigma=lambda=0.2 and mean reversion speed theta=0.3. After some trying around I merely managed to generate numbers very close to the listed ones with unchanged theta and sigma, but on a completely different tenor structure given by {0.7, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0}.As several different independent implementations gave the same results, I am pretty positive that my code is flawless.Has anyone successfully or unsuccessfully worked with this formula already and can confirm these problems? Or am I still missing a point?Any kind of help would be highly appreciated.Thanks,MAOL

Maol,very interesting. I have not tried yet, but looking at the numbers I also doubt that the tenor times given make sense. If you have 75% vol for the first week and 95% vol for the rest of the first year, an effective vol of 81% seems too low for me.

Yes, those numbers dont align with the papers exemplar data.Tried this myself and can invalidate Mr Piterbargs numbers.Also, volvol homogenozation quite prone to instability. IMO better hands off and try with homogeneous volvol (ie const) across time instead.Rgds

can I hav access to the paper?regardscosmo

I'll double-check and revert back.Thanks for pointing out potential issues with the numbersI disagree with "Arnheim" who states that "volvol homogenozation quite prone to instability", I have never had any problems-Vladimir

All,The confusion seems to arise from the fact that the effective vol of variance (same for vol and skew) is NOT piecewise constant between the reported time points (0.02,1,2,...,7) but in fact is interpolated. Here is the procedure in a bit more detail1. Take term (ie effective) vol of var as given in the table2. Interpolate (cubic) with dt = 1m3. Compute inst vol of var for all monthly points using the equations from the paper4. Report the results for t=0.02, 1,2,...,7To answer GoGoFa's point, the procedure above makes it plain that the inst vol of variance is essentially interpolated from 75% at t=0.02 to 95% at t=1. The simple arithmetic average of the two numbers is 85%, which is quite close to 81% reported, so no mystery here.While I reiterate that I did not have any problems with instabilities in vol of var calibration (it is a linear problem, after all), I do agree with Arnheim that it is better to use constant, or nearly constant, vol of vars -- this can be achieved by the use of the mean reversion of volatility parameter theta-V