We propose novel nonparametric estimators for stochastic volatility and the volatility of volatility. In doing so, we relax the assumption of a constant volatility of volatility and therefore, we allow the volatility of volatility to vary over time. Our methods are exceedingly simple and far...

We present a formal theorem of the square root of the Brownian motion. In doing so, we show that this process can be presented as a typical complex random variable. In addition, we introduce the basic properties of this process