Stochastic Differential Equation Model for Detecting Digital Currency Market Manipulation: A Systematic Review

  • Lei Shen School of Finance and Mathematics, Huainan Normal University, Huainan, 232038, China
  • Hanqiao Tang School of Education, Huainan Normal University, Huainan, 232038, China
Article ID: 3728
DOI: https://doi.org/10.59400/adecp3728
Keywords: change-point detection; Cryptocurrency markets; market manipulation; stochastic differential equations; volatility modelling

Abstract

Digital currency markets exhibit extreme volatility, heavy tails, and bursty order-flow that complicate surveillance and heighten manipulation risk. This systematic review synthesizes the state of the art in stochastic differential equation (SDE)–based approaches for detection and monitoring of abusive practices in cryptocurrencies. Following PRISMA 2020 and PICOS, an Elsevier-indexed search (2015–2025) yielded 273 records; after screening and eligibility assessment, 20 primary studies (2018–2025) were included. The literature clusters into six methodological families: (i) stochastic volatility and jump–diffusion models for heavy-tailed returns and volatility smiles; (ii) Hawkes and related point-process models for clustered order arrivals, spoofing, pump-and-dump, and wash trading; (iii) Markov and regime-switching diffusions that delineate latent “fair” versus manipulated regimes; (iv) hybrid SDE–machine learning frameworks for high-frequency prediction; (v) change-point and sequential detection methods grounded in likelihood ratios and optimal stopping; and (vi) meta-studies consolidating performance trends. Across studies, Hawkes-type intensities consistently outperform Poisson and threshold baselines in event detection; regime-switching models align with known market breaks; and hybrid neural–SDE systems achieve the strongest forecasting but at reduced interpretability. We formalize a taxonomy linking model structure to surveillance objective, and we delineate a practical trade-off between transparency (classical SDEs) and predictive accuracy (hybrid models). The review highlights open needs in explainable hybrid designs, reproducible datasets, and real-time deploy ability for exchanges and regulators. By connecting applied probability, financial engineering, and control, the paper clarifies how SDE frameworks can underpin robust, auditable market-integrity tools for digital assets.

Published
2025-09-28
How to Cite
Shen, L., & Tang, H. (2025). Stochastic Differential Equation Model for Detecting Digital Currency Market Manipulation: A Systematic Review. Advances in Differential Equations and Control Processes, 32(3). https://doi.org/10.59400/adecp3728
Issue
Vol. 32 No. 3 (2025)
Section
Review
Supporting Agencies

This article is supported by the Anhui Provincial University Philosophy and Social Science Research Project “Research on the Digital Transformation and Development of the Anhui Provincial Supply and Marketing Cooperative Oriented towards Rural Revitalization” (Project No.: 2023AH051508), “Research on the Innovation of the Precise Supply Mechanism of Compulsory Education under the New Trend of Population Structure” (Project No.: 2024AH053242), and “Research on the Model, Spatio-Temporal Characteristics, Influencing Factors and Path Optimization of the Integration of Agriculture and Tourism in the Huaihe River Ecological Economic Belt under the Background of Rural Revitalization” (Project No.: 2023AH051512).

Copyright (c) 2025 Lei Shen, Hanqiao Tang

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

References

[1]Mehta K, Chawla S. Illuminating the dark corners: a qualitative examination of cryptocurrency’s risk. Digital Policy, Regulation and Governance. 2024;26(2):188-208. doi:10.1108/DPRG-10-2023-0147

[2]Fletcher E, Larkin C, Corbet S. Countering money laundering and terrorist financing: A case for bitcoin regulation. Res Int Bus Finance. 2021;56. doi: 10.1016/j.ribaf.2021.101387

[3]Jackon G. Cryptocurrency Adoption in Traditional Financial Markets in the United States. American Journal of Finance. 2024;9(1):40-50. doi:10.47672/ajf.1810

[4]Nguyen LTM, Nguyen PT. Do crypto investors wait and see during policy uncertainty? An examination of the dynamic relationships between policy uncertainty and exchange inflows of Bitcoin. Review of Behavioral Finance. 2024;16(2):234-247. doi:10.1108/RBF-01-2023-0013

[5]Donier J, Bouchaud JP. Why do markets crash? Bitcoin data offers unprecedented insights. PLoS One. 2015;10(10). doi: 10.1371/journal.pone.0139356

[6]Asafo-Adjei E, Owusu Junior P, Adam AM. Information Flow between Global Equities and Cryptocurrencies: A VMD-Based Entropy Evaluating Shocks from COVID-19 Pandemic. Complexity. 2021;2021. doi:10.1155/2021/4753753

[7]Aslanidis N, Bariviera AF, López ÓG. The link between Bitcoin and Google Trends attention. Published online June 13, 2021. http://arxiv.org/abs/2106.07104

[8]Erfanian HR, Hajimohammadi M, Abdi MJ. Using the euler-maruyama method for finding a solution to stochastic financial problems. International Journal of Intelligent Systems and Applications. 2016;8(6):48-55. doi:10.5815/ijisa.2016.06.06

[9]To Cheung K. Application and Empirical Analysis of Random Volatility Model in Financial Markets. Vol 2024.; 2024.

[10]Houssam B. A Fractional Volatility Model: Estimation of the NASDAQ volatility parameter using Futures pricing. Preprint posted online April 29, 2025. doi:10.21203/rs.3.rs-6547415/v1

[11]Han J, Zhang XP, Wang F. Gaussian Process Regression Stochastic Volatility Model for Financial Time Series. IEEE J Sel Top Signal Process. 2016;10(6):1015-1028. doi:10.1109/JSTSP.2016.2570738

[12]Fang G, Ma H, Xia M, Zhang B. The FFBS Estimation of High Dimensional Panel Data Factor Stochastic Volatility Models. Published online April 8, 2019. http://arxiv.org/abs/1901.10516

[13]Hossain MJ, Ismail MT. Is there any influence of other cryptocurrencies on bitcoin? Asian Academy of Management Journal of Accounting and Finance. 2021;17(1):125-152. doi:10.21315/aamjaf2021.17.1.5

[14]He Y. Bitcoin Volatility in Web 3.0 and Revelation to Digital Currency. Vol 2023.; 2024.

[15]Kim J, Yoon J, Yu S. Multiscale Stochastic Volatility with the Hull–White Rate of Interest. Journal of Futures Markets. 2014;34(9):819-837. doi:10.1002/fut.21625

[16]Dhifaoui Z. Determinism and Non-linear Behaviour of Log-return and Conditional Volatility: Empirical Analysis for 26 Stock Markets. South Asian Journal of Macroeconomics and Public Finance. 2022;11(1):69-94. doi:10.1177/2277978721995654

[17]Burtnyak I, Malytska A. Cev Model with Stochastic Volatility. Journal of Vasyl Stefanyk Precarpathian National University. 2019;6(3-4):22-28. doi:10.15330/jpnu.6.3-4.22-28

[18]Billio M, Sartore D. Stochastic Volatility Models: A Survey with Applications to Option Pricing and Value at Risk. In: Applied Quantitative Methods for Trading and Investment. Wiley; 2003:239-291. doi: 10.1002/0470013265.ch8

[19]Withanawasam RM, Whigham PA, Crack TF, Premachandra IM. Simulating Trader Manipulation in a Limit-Order Driven Market.; 2011. http://mssanz.org.au/modsim2011

[20]Swishchuk A, Vadori N. A Semi-Markovian Modeling of Limit Order Markets. Published online January 7, 2016. http://arxiv.org/abs/1601.01710

[21]Bacry E, Jaisson T, Muzy J. Estimation of slowly decreasing Hawkes kernels: application to high-frequency order book dynamics. Quant Finance. 2016;16(8):1179-1201. doi:10.1080/14697688.2015.1123287

[22]Bacry E, Mastromatteo I, Muzy JF. Hawkes processes in finance. Published online May 17, 2015. http://arxiv.org/abs/1502.04592

[23]Cao Y, Li Y, Coleman S, Belatreche A, Mcginnity TM. Detecting Price Manipulation in the Financial Market.

[24]Kaj I, Caglar M. A buffer Hawkes process for limit order books. Published online October 10, 2017. http://arxiv.org/abs/1710.03506

[25]Fry J. Booms, Busts and Heavy-Tails: The Story of Bitcoin and Cryptocurrency Markets? 2018.

[26]Dipple S, Choudhary A, Flamino J, Szymanski BK, Korniss G. Using correlated stochastic differential equations to forecast cryptocurrency rates and social media activities. Appl Netw Sci. 2020;5(1). doi:10.1007/s41109-020-00259-1

[27]Chen KS, Huang YC. Detecting jump risk and jump-diffusion model for bitcoin options pricing and hedging. Mathematics. 2021;9(20). doi:10.3390/math9202567

[28]Kalariya V, Parmar P, Jay P, et al. Stochastic Neural Networks-Based Algorithmic Trading for the Cryptocurrency Market. Mathematics. 2022;10(9). doi:10.3390/math10091456

[29]Kurbucz MT, Pósfay P, Jakovác A. Linear Laws of Markov Chains with an Application for Anomaly Detection in Bitcoin Prices. Published online January 24, 2022. http://arxiv.org/abs/2201.09790

[30]Ortu M, Vacca S, Destefanis G, Conversano C. Cryptocurrency ecosystems and social media environments: An empirical analysis through Hawkes’ models and natural language processing. Machine Learning with Applications. 2022; 7:100229. doi: 10.1016/j.mlwa.2021.100229

[31]El-Khatib Y, Hatemi-J A. On a Regime Switching Illiquid High Volatile Prediction Model for Cryptocurrencies. Vol 16.; 1145.

[32]La Morgia M, Mei A, Sassi F, Stefa J. The Doge of Wall Street: Analysis and Detection of Pump and Dump Cryptocurrency Manipulations. ACM Trans Internet Technol. 2023;23(1). doi:10.1145/3561300

[33]Theodosiadou O, Koufakis AM, Tsikrika T, Vrochidis S, Kompatsiaris I. Change Point Analysis of Time Series Related to Bitcoin Transactions: Towards the Detection of Illegal Activities. Journal of Risk and Financial Management. 2023;16(9). doi:10.3390/jrfm16090408

[34]Lukić Ž, Milošević B. Change point analysis -- the empirical Hankel transform approach. Published online December 31, 2023. http://arxiv.org/abs/2401.00566

[35]Zournatzidou G, Farazakis D, Mallidis I, Floros C. Stochastic Patterns of Bitcoin Volatility: Evidence across Measures. Mathematics. 2024;12(11). doi:10.3390/math12111719

[36]Fabre T, Toke IM. Neural Hawkes: Non-Parametric Estimation in High Dimension and Causality Analysis in Cryptocurrency Markets. Published online November 4, 2024. doi:10.1080/14697688.2025.2477673

[37]Harasheh M, Bouteska A. Volatility estimation through stochastic processes: Evidence from cryptocurrencies. North American Journal of Economics and Finance. 2025;75. doi: 10.1016/j.najef.2024.102320

[38]Luo R, Krishnamurthy V. Detecting Structural Shifts in Multivariate Hawkes Processes with Fréchet Statistics. Published online January 22, 2025. http://arxiv.org/abs/2308.06769

[39]Fabre T, Toke IM. High-Frequency Market Manipulation Detection with a Markov-modulated Hawkes process. Published online February 6, 2025. http://arxiv.org/abs/2502.04027

[40]Fabre T, Challet D. Learning the Spoofability of Limit Order Books With Interpretable Probabilistic Neural Networks. Published online April 22, 2025. http://arxiv.org/abs/2504.15908

[41]Avordeh TK, Arthur S, Quaidoo C. Hybrid machine learning and stochastic volatility models with blockchain data for high-frequency cryptocurrency trading. Preprint posted online April 2, 2025. doi:10.21203/rs.3.rs-6352921/v1

[42]Pindza E, Clement J, Mwambi S, Umeorah N. Neural Network for Valuing Bitcoin Options Under Jump-Diffusion and Market Sentiment Model. Comput Econ. Published online 2024. doi:10.1007/s10614-024-10792-1

[43]Pakštaitė V, Filatovas E, Juodis M, Paulavičius R. Bitcoin Price Regime Shifts: A Bayesian MCMC and Hidden Markov Model Analysis of Macroeconomic Influence. Mathematics. 2025;13(10). doi:10.3390/math13101577

[44]Dote-Pardo J, Espinosa-Jaramillo MT. Mathematical Models in Cryptocurrency Markets and Decentralized Finance (DeFi): Pricing, Risk, and Network Dynamics. https://ssrn.com/abstract=5248613