Re: [Quantlib-users] QuantLib's GBM found flawed. What say the experts?

[U.Mutlu <um...@mu...>]

I think Ito's lemma is the big culprit here. Ito's lemma is IMO
misused in the whole field, and should especially not be used
in GBM since GBM uses timeSteps...

I'm 100% sure that one really does not need this Ito's lemma stuff,
neither in GBM nor in the Black-Scholes-Merton (BSM) option pricing formula.
Dunno about fields beyond these 2 cases.

Just ask me if you need a proof for the BSM case.

The GBM case (using the standard GBM algoritm with Ito's lemma)
was proven to be incorrect just some weeks ago, again by me:
https://www.elitetrader.com/et/threads/simulating-stock-prices-using-gbm.375533/page-3#post-5849548
https://www.elitetrader.com/et/threads/simulating-stock-prices-using-gbm.375533/page-4#post-5851336

I wonder why the academia favors and is using this Ito's lemma stuff,
as it's really unnecessary, IMO.


Peter Caspers wrote on 09/09/23 20:24:
> Also notice that the (Ito-) solution of the SDE of
> GeometricBrownianMotionProcess
>
>              dS(t, S)= \mu S dt + \sigma S dW_t.
>
> see here
>
> https://github.com/OpenSourceRisk/QuantLib/blob/00d2fced875622c1f52d9025b3ab01d04729eee8/ql/processes/geometricbrownianprocess.hpp#L36
>
> is lognormally distributed with parameters
>
> ln S(t) ~ N( \mu * t - 0.5 * \sigma^2 * t, \sigma^2 * t ).
>
> Your testing code seems to assume
>
> ln S(t) ~ N( \mu, \sigma^2 * t).
>
> on the other hand. So maybe this is just a misunderstanding of the
> parameters going into the constructor of
> GeometricBrownianMotionProcess?
>
> Best
> Peter
>
> On Sat, 9 Sept 2023 at 16:45, Ioannis Rigopoulos <qua...@de...> wrote:
>>
>> If you search within the QuantLib code for BoxMullerGaussianRng, you
>> will see it is used only in the experimental folder. It is therefore not
>> surprising if it doesn't produce the expected results.
>>
>> I use myself the MultiPathGenerator with PseudoRandom::rsg_type, which
>> is used extensively in other areas of QuantLib.
>>
>> This type expands to InverseCumulativeRsg< RandomSequenceGenerator<
>> MersenneTwisterUniformRng > , InverseCumulativeNormal > and gives me
>> good results.
>>
>> Ioannis Rigopoulos, founder of deriscope.com
>>
>> On 9/9/2023 11:25 AM, U.Mutlu wrote:
>>> A short standalone test code in C++ with test results posted online at
>>> https://www.elitetrader.com/et/threads/simulating-stock-prices-using-gbm.375533/page-4#post-5861368
>>>
>>> demonstrates that the GBM method in QuantLib
>>> is fatally buggy and has been so since start.
>>>
>>> Can the experts please check it and comment it.
>>> It's suspicious that such a flaw in a very important part of the
>>> library (GBM and Monte Carlo)
>>> got undetected by the experts and the user community for more that 20+
>>> years.
>>>
>>> Can the experts verify / confirm / duplicate the findings made there?
>>> Or is maybe that test code itself buggy or the test method maybe
>>> unscientific?
>>>
>>>
>>>
>>> _______________________________________________
>>> QuantLib-users mailing list
>>> Qua...@li...
>>> https://lists.sourceforge.net/lists/listinfo/quantlib-users
>>
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