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I hear that there are many extensions to the black scholes model to make it more realistic, however, GBM does not account for volatile swings. Is there any sort of alternative approach to use instead?

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    $\begingroup$ There are many, many alternatives. Best you start looking into stochastic volatility models (e.g. Heston 1993). But you should first read a bit about them online and then ask a more precise question here. $\endgroup$ – KeSchn Jul 3 at 23:15