# Random Walk for Asset

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