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Dynamics of Moving Average Rules in a Continuous-time Financial Market Model

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Abstract

Within a continuous-time framework, this paper proposes a stochastic heterogeneous agent model (HAM) of financial markets with time delays to unify various moving average rules used indiscrete-time HAMs. The time delay represents a memory length of a moving average rule indiscrete-time HAMs.Intuitive conditions for the stability of the fundamental price of the deterministic model in terms of agents' behavior parameters and memory length are obtained. It is found that an increase in memory length not only can destabilize the market price, resulting in oscillatory market price characterized by a Hopf bifurcation, but also can stabilize another wise unstable market price, leading to stability switching as the memory length increases. Numerical simulations show that the stochastic model is able to characterize long deviations of the market price from its fundamental price and excess volatility and generate most of the stylized factso bserved in financial markets.

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  • Xue-Zhong He & Min Zheng, 2010. "Dynamics of Moving Average Rules in a Continuous-time Financial Market Model," Research Paper Series 268, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:268
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    1. Gori, Luca & Guerrini, Luca & Sodini, Mauro, 2015. "A continuous time Cournot duopoly with delays," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 166-177.
    2. Luca Gori & Luca Guerrini & Mauro Sodini, 2014. "Heterogeneous Fundamentalists in a Continuous Time Model with Delays," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-6, August.
    3. Yan, Tingjin & Chiu, Mei Choi & Wong, Hoi Ying, 2023. "Portfolio liquidation with delayed information," Economic Modelling, Elsevier, vol. 126(C).
    4. He, Xue-Zhong & Li, Kai, 2012. "Heterogeneous beliefs and adaptive behaviour in a continuous-time asset price model," Journal of Economic Dynamics and Control, Elsevier, vol. 36(7), pages 973-987.
    5. Guo, Bin & Zhang, Wei & Chen, Shu-Heng & Zhang, Yongjie, 2015. "The optimal pricing of a market maker in a heterogeneous agent economy," Finance Research Letters, Elsevier, vol. 14(C), pages 178-187.
    6. Wang, Lijun & An, Haizhong & Liu, Xiaojia & Huang, Xuan, 2016. "Selecting dynamic moving average trading rules in the crude oil futures market using a genetic approach," Applied Energy, Elsevier, vol. 162(C), pages 1608-1618.
    7. Zsolt Bihary & Attila Andr'as V'ig, 2019. "Analytic solutions in a continuous-time financial market model," Papers 1902.09999, arXiv.org.
    8. Lijun Wang & Haizhong An & Xiaohua Xia & Xiaojia Liu & Xiaoqi Sun & Xuan Huang, 2014. "Generating Moving Average Trading Rules on the Oil Futures Market with Genetic Algorithms," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-10, May.
    9. Di Guilmi, Corrado & He, Xue-Zhong & Li, Kai, 2014. "Herding, trend chasing and market volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 349-373.
    10. Luca Guerrini & Akio Matsumoto & Ferenc Szidarovszky, 2018. "A heterogeneous agent model of asset price dynamics with two time delays," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 379-397, November.
    11. Xue-Zhong He, 2012. "Recent Developments on Heterogeneous Beliefs and Adaptive Behaviour of Financial Markets," Research Paper Series 316, Quantitative Finance Research Centre, University of Technology, Sydney.
    12. Sandrine Jacob Leal, 2015. "Fundamentalists, Chartists and Asset pricing anomalies," Post-Print hal-01508002, HAL.
    13. Akio Matsumoto & Ferenc Szidarovszky, 2024. "Nonlinear Kaldor model augmented with retardation and anticipation," Annals of Operations Research, Springer, vol. 337(3), pages 937-958, June.
    14. Bihary, Zsolt & Víg, Attila András, 2020. "Heterogén kereskedési stratégiák hatása a piaci árfolyamokra [The effect of heterogeneous commercial strategies on market exchange rates]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 688-707.
    15. Kai Li, 2014. "Asset Price Dynamics with Heterogeneous Beliefs and Time Delays," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 13, July-Dece.
    16. Kai Li, 2014. "Asset Price Dynamics with Heterogeneous Beliefs and Time Delays," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2014, January-A.
    17. Din Prathumwan & Kamonchat Trachoo, 2019. "Application of the Laplace Homotopy Perturbation Method to the Black–Scholes Model Based on a European Put Option with Two Assets," Mathematics, MDPI, vol. 7(4), pages 1-11, March.
    18. Roberto Dieci & Xue-Zhong He, 2021. "Cross-section instability in financial markets: impatience, extrapolation, and switching," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 727-754, December.
    19. Sandrine Jacob Leal, 2015. "Fundamentalists, chartists and asset pricing anomalies," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1837-1850, November.
    20. Din Prathumwan & Wannika Sawangtong & Panumart Sawangtong, 2017. "An Analysis on the Fractional Asset Flow Differential Equations," Mathematics, MDPI, vol. 5(2), pages 1-17, June.

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