On the Numerical Option Pricing Methods: Fractional Black-Scholes Equations with CEV Assets

This article explores a stochastic volatility model that incorporates fractional Brownian motion (fBm) into the constant elasticity of variance (CEV) framework. We use time series models to estimate the drift and volatility parameters of the model and validate its performance. We also examine the fractional Black-Scholes (BS) equation arising from the CEV model with fBm. To solve this equation numerically, we apply a Chebyshev collocation method and analyze its convergence properties. We demonstrate the effectiveness of the numerical method with an example and apply it to the option pricing problem.