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Option pricing in stochastic volatility models driven by fractional Lévy processes

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  • Zhigang Tong

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.

Suggested Citation

  • Zhigang Tong, 2016. "Option pricing in stochastic volatility models driven by fractional Lévy processes," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 5(1), pages 56-75.
    • Handle: RePEc:ids:ijfmkd:v:5:y:2016:i:1:p:56-75
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    References listed on IDEAS

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    8. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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    Cited by:

    1. Wang, XiaoTian & Yang, ZiJian & Cao, PiYao & Wang, ShiLin, 2021. "The closed-form option pricing formulas under the sub-fractional Poisson volatility models," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).

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