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 |