Multiplicative Langevin Process for Volatilities Produces Observed Q-Variance Regularities

William H. Press, Alex Dannenberg

Q-variance (so-called) posits a statistical relationship $\mathbf{E}({\sigma }^2|z)={\sigma }_0^2+\frac{1}{2}{z}^2$ between an asset's volatility ${\sigma }^2$, as observed in a time interval $T$, an…