Option Pricing and Risk Management under Fractional Brownian Motion with Stochastic Volatility

This paper delves into the pricing and hedging of financial derivatives within the framework of fractional Brownian motion (fBM). Traditional models often fall short in capturing market realities, particularly the long-memory and self-similarity characteristics inherent in asset prices and volatility. To address this, we extend classical option pricing theory by integrating tools from Malliavin calculus, offering a nuanced treatment of stochastic volatility under fBM. A Riccati equation governs the resulting model, allowing for analytical and numerical solutions that align with observed market behavior. Furthermore, we propose a correction term to account for residual volatility risk, providing a more practical approach to hedging. This study bridges theoretical advancements with empirical applicability, laying the groundwork for future exploration of fBM-driven financial models. JEL Classification. G13, G17, C61.