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

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

Thank you very much Jack for this clarification.
Unfortunately for us the Andreasen Huge yields very poor results on a well
behaved SPX surface.
As a consequence we will have to get out of the entire QL ecosystem as
nothing beyond a vanilla call and put can be priced.
Thanks for your help again.

On Tue, Jan 3, 2023 at 9:39 PM Jack G <jac...@gm...> wrote:

> Hi Dan,
>
> Looking over my notes, here is what we did:
>
> - Calibrated a local vol surface within QL using Andreasen Huge. This
> didn't cause problems for us but the vol surfaces were quite well behaved -
> we were using FX data from Bloomberg, the main data issues were around FX
> quoting conventions as I recall
> - Fitted raw Heston to the data (we didn't use PWC Heston in the end as
> discussed previously)
> - Calibrated a leverage function (note the AH instantaneous vol surface
> was used here not the surface itself), I see we tried both FD and MC
> calibrations, and calibrated mixing factors too to a selection of DNTs (I
> recall there was a bug in one of the QL calibrations which was ignoring
> mixing factor that we fixed around that time)
> - Tested the leverage function against vanillas using FdHestonVanillaEngine
> which admits a leverage function, and tested various MC prices using HestonSLVProcess,
> both of these engines do not rely on the Andraesen Huge calibrated object
> directly, only on the leverage function calibrated from it
>
> All the best,
> Jack
>
> On Sat, Dec 31, 2022 at 12:16 AM Dan VolPM <dan...@gm...> wrote:
>
>> 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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>>>>>