Rough volatility models

Abstract

This project examines the limitations of the Black-Scholes model in replicating the empirical properties of real market data and introduces rough volatility models as a superior alternative. The Black-Scholes model assumes normally distributed returns and constant volatility, failing to capture the heavy tails and volatility clustering observed in financial markets, making it unsuitable for accurate option pricing. Because of this, financial practitioners have switched their focus to developing alternatives to traditional models, one being rough volatility models. These models incorporate fractal behavior and rough paths in volatility, demonstrating an improvement in replicating market dynamics. This project aims to analyze models based on rough volatilities through their application in option pricing and the computation of implied volatilities. The results indicate that rough volatility models improve on the shortcomings of the Black-Scholes model.