A Lévy-Itô model driven by approximate Riemann-Liouville fractional Brownian motions for pricing financial derivatives

We propose a new general risky asset price model for pricing financial derivatives in this article. It is a Lévy-Itô type of jump diffusion model with a semimartingale approximation of fractional stochastic volatility and jump intensity. This model allows the pure stochastic volatility and the jump intensity components to be functions of fast and slowly varying stochastic processes driven by an approximate form of Riemann-Liouville fractional Brownian motion. We derive a system of partial integro-differential equations for the price of European derivatives via the asymptotic expansion method and use Fourier analysis to obtain an explicit pricing formula which can easily be calculated once the (generalized) Fourier transform of the payoff function is obtained. Based on this mathematical formula, we find that the proposed model outperforms the benchmark models in terms of implied volatility fit, which is more conspicuous when time-to-maturity is relatively short.