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 |