Title: Option pricing in stochastic volatility models driven by fractional Lévy processes

Authors: Zhigang Tong

Addresses: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

Abstract: In this paper, we propose a continuous time fractional stochastic volatility model which extends the Barndorff-Nielsen and Shephard (2001) (BNS) model. Our model is the fractional BNS model, where we model the volatility as a fractional Lévy-driven Ornstein-Uhlenbeck process. We allow the memory parameter to be flexible so that our model can potentially produce short- or long-memory in volatility. We derive the analytical formula for option pricing using Fourier inversion technique. We numerically study the effect of memory parameter on the option prices and the calibration result indicates that the fractional model significantly improves the performance of the original BNS model.

Keywords: option pricing; stochastic volatility; Levy-driven OU process; fractional Levy; fractional calculus; volatility models; stochastic modelling; Fourier inversion; options.

DOI: 10.1504/IJFMD.2016.076983

International Journal of Financial Markets and Derivatives, 2016 Vol.5 No.1, pp.56 - 75

Received: 28 Oct 2015
Accepted: 20 Feb 2016
Published online: 16 Jun 2016 *

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