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European Option Pricing Based on FSDE Driven by Fractional Brownian Motion
- 1 Jiangxi University of Finance and Economics
* Author to whom correspondence should be addressed.
Abstract
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.
Keywords
European option pricing, Fractional stochastic differential equations, Fractional Brownian motion, Hurst index, Empirical research
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Cite this article
Shu,Q. (2024). European Option Pricing Based on FSDE Driven by Fractional Brownian Motion . Theoretical and Natural Science,34,118-133.
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Volume title: Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
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