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Take the analogy of equations modelling something in physics. Just because you write down an equation, it does not mean it has to be connected to anything in reality. It only do so to the extent you have adapted the equation and it's parameters to fit reality. In finance things are a bit more complicated when it comes to the predicting power though. ...


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The GBM model is liked by practitioners for the modelling of stock prices for the following reasons: (i) The solution is log-normal, so the stock price distribution varies between zero and infinity: which is what we would expect from a real-world stock price. (ii) The model has independent increments, which means the future distribution of the stock only ...


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The SDE you are describing is called the Geometric Brownian Motion. In the end its just a model, which underlies certain assumptions, which are usually not met in the real world scenarios. There are many further extensions and variation of SDEs for modelling prices f.e. including a jump component (jump diffusion models), mean reversion (f.e. Ornstein-...


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