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

[Peter C. <pca...@gm...>]

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?
> >
> >
> >
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>
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