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 overcome the limitations of the previous literature in the European options pricing. In doing so, we provide a closed-form formula that doesn't require any numerical/computational methods. The formula is as simple as the classical Black-Scholes pricing formula. In addition, we simultaneously...

We overcome a major obstacle in the literature. In doing, we introduce a simple, closed-form formula for pricing the American options. In particular, we significantly simplify Alghalith's closed-form formula for pricing American options. In doing so, we introduce a formula that does not require...

We introduce a novel and convenient approach to utility modeling. In doing so, we present a general utility function in a very simple exact form. Furthermore, we develop a method to (accurately) measure preferences without any utility data. We also devise a method to measure the marginal...

We present simple parametric methods that overcome major limitations of the literature on joint/marginal density estimation. In doing so, we do not assume any form of marginal or joint distribution. Furthermore, using our method, a multivariate density can be easily estimated if we know only one...

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...