Financial volatility ($\sigma$)

Financial volatility quantifies variability of asset returns. In the Black-Scholes model, $\sigma$ is the coefficient of the Brownian increment in the stock return $d{S}_t/S_t=\mu dt+\sigma d{W}_t$, so its instantaneous log-return variance rate is ${\sigma }^2$. For deterministic time-varying volatility, the variance over an interval is the integral of that squared coefficient.