École Nationale Supérieure de
Techniques Avancées

Abstract

In this paper, we delve into stochastic volatility models driven by fractional Brownian motion and draw a comparison with conventional models, with mainly emphasis on the Heston model type. We provide historical evidence and conduct an in-depth investigation into Analytical Pricing and Monte-Carlo Pricing techniques to validate the stylized facts as described in the works of Omar El Euch, Mathieu Rosenbaum, and Jim Gatheral. Furthermore, we perform calibration using SX5E index market data to gain insights into the behavior of rough stochastic volatility models.