Long-Memory Option Pricing: A Comparison Based on Fractional Brownian Motion and the Black-Scholes Model

DOI

10.2991/978-94-6239-801-6_34How to use a DOI?

Keywords

Long-Range Memory; Fractional Brownian Motion; Black-Scholes Model; Hurst Index

Abstract

Distribution properties of asset returns and assets market volatility are among the fundamental aspects that affect option pricing. Typically, these factors vary with the different market conditions thus creating biases in the conventional pricing models. The traditional Black-Scholes model is based on the assumption that the returns of the assets are characterized by the random walk, however, the empirical studies have shown that markets are often fractal. This paper analyses Shanghai Composite Index. Once the non-normality of return sequences has been established, it proves that the market is highly long memory (H > 0.5). Upon this, an option-based pricing model based on a fractional Brownian motion is built and the model is simulated against the traditional one. Findings reveal that the long memory fractional B-S model is much more effective when compared to the classical one in pricing long- run options, which best capture the actual volatility risk in the market. The given study enhances empirical evidence to the option pricing theory under fractal market theory, offering more practical theoretical backgrounds and methodological references to the option trading decisions of the long-term investors and the optimization procedure of the risk management of financial institutions.

Copyright

© 2026 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Jinglong Yu
PY  - 2026
DA  - 2026/10/23
TI  - Long-Memory Option Pricing: A Comparison Based on Fractional Brownian Motion and the Black-Scholes Model
BT  - Proceedings of the 2026 2nd International Conference on Financial Innovation and Marketing Management (FIMM 2026)
PB  - Atlantis Press
SP  - 301
EP  - 309
SN  - 2352-5428
UR  - https://doi.org/10.2991/978-94-6239-801-6_34
DO  - 10.2991/978-94-6239-801-6_34
ID  - Yu2026
ER  -