Theoretical and Natural Science

- The Open Access Proceedings Series for Conferences

Theoretical and Natural Science

Vol. 34, 02 April 2024

Open Access | Article

European Option Pricing Based on FSDE Driven by Fractional Brownian Motion

Qingyang Shu * 1
1 Jiangxi University of Finance and Economics

* Author to whom correspondence should be addressed.

Advances in Humanities Research, Vol. 34, 118-133
Published 02 April 2024. © 2023 The Author(s). Published by EWA Publishing
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citation Qingyang Shu. European Option Pricing Based on FSDE Driven by Fractional Brownian Motion . TNS (2024) Vol. 34: 118-133. DOI: 10.54254/2753-8818/34/20241190.


In the actual financial market, the classical Black-Scholes (B-S) model can’t perfectly describe the process of stock price. Besides, memory effect is an important phenomenon in financial systems. Thus, in this paper, we establish a fractional order stochastic differential equations (FSDE) which is driven by fractional Brownian motion (fBm) to describe the effect of noise memory and trend memory in financial pricing. Finally, we derive a European option pricing formula based on the established model. After conducting an empirical analysis based on the SSE 50ETF, we find that the established model performs better than the traditional one.


European option pricing, Fractional stochastic differential equations, Fractional Brownian motion, Hurst index, Empirical research


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Data Availability

The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

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Volume Title
Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
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Published Date
02 April 2024
Theoretical and Natural Science
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© 2023 The Author(s)
Open Access
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Copyright © 2023 EWA Publishing. Unless Otherwise Stated