Financial Modeling under Rough and Fractional Stochastic Volatility

Volatility, usually denoted by σ, is a measure of the amount of fluctuation in asset prices and so it is often understood or perceived as a measure of riskiness of the asset or uncertainty about its future value. Since there are various ways one can quantify this risk, a comprehensive and precise study of this quantity is needed. For this reason there are various definitions of volatility, based on the framework and on the purpose of the model.