# Itô integrals for fractional Brownian motion and applications to option pricing

@article{Qian2018ItIF, title={It{\^o} integrals for fractional Brownian motion and applications to option pricing}, author={Zhongmin Qian and Xingcheng Xu}, journal={arXiv: Probability}, year={2018} }

In this paper, we develop an It\^o type integration theory for fractional Brownian motions with Hurst parameter $H\in(\frac{1}{3},\frac{1}{2})$ via rough path theory. The It\^o type integrals are path-wise defined and have zero expectations. We establish the fundamental tools associated with this It\^o type integration such as It\^o formula, chain rule and etc. As an application we apply this path-wise It\^o integration theory to the study of a fractional Black-Scholes model with Hurst…

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