[Quantlib-users] Problem with LocalVol and Piecewise Time Dependent Heston processes

[Dan V. <dan...@gm...>]

Hello experts,

Has anyone been able to price any product in monte carlo (generating path
via the GaussianMultiPathGenerator) using either a local vol surface or a
piecewise Heston ?
I should mention we used python.

*The problems with LocalVol is:*
- Only the AndreasenHugeVolatility does not break when generating paths,
however there is such a loss of information in the process of building it
that the prices generated are extremely far from the calibrating vanillas
- Whenever we use our (smoothed and cleaned) BlackVarianceSurface and
generate paths with it, it is converted into a localvol surface under the
cover which is perfect for path generation BUT it is virtually impossible
to actually get paths that don't break on "arbitrages". I use the quote
there  for arbitrage because the test used is so granular that converting
any kind of real life market surface will fail (I'm not talking here about
the 4x4 matrices that we all use for examples but rather a huge SPX surface
with tons of strikes and maturities). Even an SVI failed at that which is
telling me either we do something very wrong or the falling var and fly
testing is just too granular.

=> this leaves us stuck unable to price any non standard payoff in LV

*The problem with PTD Heston is:*
- It takes forever to calibrate and still has a pretty poor quality of fit
- there is no way to build a PTDHeston process like there is for regular
Heston. Consequently building paths is just impossible.

Is there a different way to go about pricing non standard payoffs using one
of these 2 methods ?
Happy to hear from someone who can actually make it work.

Any help would be greatly appreciated.
Thank you