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

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

Hi Jack,
You mean that you built both your own LV surface outside of QL (since QL
won't let you build a correct one) as well as calibrating the PTD Heston
outside of QL ?
Then you fed the 2 to QL to get the leverage function and from then on
stayed in the QL ecosystem ?
Thanks
Dan

On Fri, Dec 30, 2022 at 8:24 AM Jack G <jac...@gm...> wrote:

> Hi Dan,
>
> We went with SLV in the end using plain fixed-parameter Heston and a
> leverage function (using the QuantLib calibration and path generation code).
>
> Best,
> Jack
>
> On Thu, Dec 29, 2022 at 8:01 AM Dan VolPM <dan...@gm...> wrote:
>
>> 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
>>>>
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>>>