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@jemoka / Jemoka Knowledge Base / wiki/concepts/geometric_brownian_motion.md
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--- title: "Geometric Brownian Motion" type: concept related: [Geometric Brownian Motion, Brownian Motion] source: https://www.jemoka.com/posts/kbhgeometric_brownian_motion/ confidence: high status: active --- A Geometric Brownian Motion is a Brownian Motion with a drift. It is determined by: \begin{equation} \dd{S_{t}} = \mu S_{t} \dd{t} + \sigma \dd{S_{t}} \dd{W_{t}} \end{equation} where, \(S_{t}\) is a Geometric Brownian Motion, \(\mu\) is its drift, \(\sigma\) the volatility, and \(W_{t}\) a centered Brownian Motion.