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

[Jack G <jac...@gm...>]

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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>>