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 show that, in practice, the standard unit root tests, cointegration tests, and similar tests are unreliable. This conclusion is more generally applicable to other regression-based tests. In particular, these tests attempt to solve a problem by creating another problem

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

We devise a method to circumvent the complexity that arises from the option multi-dimensionality. That is, we transform the model to make it as simple as the one-dimensional case. Furthermore, the assumption of comonotonicity and other assumptions regarding the structure of the underlying asset...

This is the first paper to provide a simple, explicit formula (that doesn’t requirenumerical/computational methods) under stochastic volatility. The formulais as simple as the classical Black-Scholes pricing formula. Furthermore,this paper modifies the Black-Scholes model to make it consistent...