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I'll add that your stock price update equation can be resolved using an Itō or Stratonovich integral. As it turns out, your equation is precisely the definition of a GeometricBrownianMotionProcess with parameters $S_0 = 32.68$, $\mu=0005214$, $\sigma=0.24$. You should simulate using the GeometricBrownianMotionProcess and not use the Wiener process directly ...

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I unfortunately don't fully understand the financial aspect of the problem, but I'm going to throw something out there, and hopefully we can improve the answer as we go. You might want to comment on this answer / edit your question as appropriate, so we can move towards a satisfactory answer. Here I generate some data points from a Wiener process ...

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Pure GammaDistribution does not seem at all like a good fit even visually. You need probably a MixtureDistribution. You could BTW skip NonlinearModelFit and start playing with FindDistributionParameters. But I think you are better of trying out latest WL function FindDistribution. In automated regime it finds almost what you need: dis = ...

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