Random Walk for Asset

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A discrete random walk for an asset can be expressed as

\[ S_{i+1} = S_{i}\Big(1 + \mu\ \delta t + \sigma\ \phi\ \delta t^{\frac{1}{2}}\Big) \]

Symbol Description
\(S_{i}\) Asset price at time step \(i\).
\(\delta t\) Size of time step
\(\mu\) Drift
\(\sigma\) Volatility
\(\phi\) A normally distributed random variable