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

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

Thank you jack.
What direction did you end up taking to price non vanilla products using QL
?

On Mon, Dec 19, 2022 at 7:24 PM Jack G <jac...@gm...> wrote:

> Hi Dan,
>
> Just for reference on the PTD Heston, adding a path generator for PTD
> Heston was something I looked at during a side project a year or so ago -
> there is some code in an abandoned pull request here but it's fairly
> horrible: https://github.com/lballabio/QuantLib/pull/1185/files
>
> In the end I found exactly the problems you have mentioned for PTD Heston
> - hard and slow to calibrate, and I wasn't getting much convergence from
> the MC prices for anything beyond vanillas. A lot of this is because
> several of the extremely useful optimizations for Heston path generation
> stop working nicely in PTD Heston.
>
> Best luck with the project,
> Jack
>
> On Tue, 20 Dec 2022, 01:24 Dan VolPM, <dan...@gm...> wrote:
>
>> 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
>>
>> _______________________________________________
>> QuantLib-users mailing list
>> Qua...@li...
>> https://lists.sourceforge.net/lists/listinfo/quantlib-users
>>
>