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Stock Price Formation: Precepts from a Multi-Agent Reinforcement Learning Model

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Abstract

In the past, the bottom-up study of financial stock markets relied on first-generation multi-agent systems (MAS) , which employed zero-intelligence agents and often required the additional implementation of so-called noise traders to emulate price formation processes. Nowadays, thanks to the tools developed in cognitive science and machine learning, MAS can quantitatively gauge agent learning, a pivotal element for information and stock price estimation in finance. In our previous work, we therefore devised a new generation MAS stock market simulator , which implements two key features: firstly, each agent autonomously learns to perform price forecasting and stock trading via model-free reinforcement learning ; secondly, all agents ’ trading decisions feed a centralised double-auction limit order book, emulating price and volume microstructures. Here, we study which trading strategies (represented as reinforcement learning policies) the agents learn and the time-dependency of their heterogeneity. Our central result is that there are more ways to succeed in trading than to fail. More specifically, we find that : i- better-performing agents learn in time more diverse trading strategies than worse-performing ones, ii- they tend to employ a fundamentalist, rather than chartist, approach to asset price valuation, and iii- their transaction orders are less stringent (i.e. larger bids or lower asks).

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References

  • Current dividend impacts of FTSE-250 stocks. (2019). https://www.dividenddata.co.uk. Accessed: 2020-05-19.

  • IG fees of Contracts For Difference. (2019). https://www.ig.com. Accessed: 2020-05-19.

  • Symba code repository. (2019). url=https://github.com/johannlussange/symba, note = Accessed: 2021-10-30.

  • UK one-year gilt reference prices. (2019). https://www.dmo.gov.uk. Accessed: 2020-05-19.

  • Aloud, M. (2014). Agent-based simulation in finance: design and choices. Proceedings in Finance and Risk Perspectives 14.

  • Barde, S. (2015). A practical, universal, information criterion over nth order markov processes. University of Kent, School of Economics Discussion Papers 04.

  • Bartolozzi, M. (2010). A multi agent model for the limit order book dynamics. The European Physical Journal B, 78(2), 265–273.

    Article  Google Scholar 

  • Benzaquen, M., & Bouchaud, J. P. (2018). A fractional reaction-diffusion description of supply and demand. The European Physical Journal B, 91(23), 1–7.

    Google Scholar 

  • Bera, A. K., Ivliev, S., & Lillo, F. (2015). Financial Econometrics and Empirical Market Microstructure. Springer.

  • Biondo, A. E. (2019). Order book modeling and financial stability. Journal of Economic Interaction and Coordination, 14(3), 469–489.

    Article  Google Scholar 

  • Boero, R., Morini, M., Sonnessa, M., & Terna, P. (2015). Agent-based models of the economy, from theories to applications. Palgrave Macmillan.

  • Bouchaud, J.-P. (2018). Chapter 7: Market Microstructure, in Computational Economics: Heterogeneous Agent Modeling, 1st Edn.

  • Bouchaud, J. P. (2019). Econophysics: Still fringe after 30 years? arXiv:1901.03691.

  • Challet, D., & Stinchcombe, R. (2003). Non-constant rates and over-diffusive prices in a simple model of limit order markets. Quantitative Finance, 3(3), 155.

    Article  Google Scholar 

  • Chen, T. T., Zheng, B., Li, Y., & Jiang, X. F. (2017). New approaches in agent-based modelling of complex financial systems. Frontiers of Physics, 12(6), 128905.

    Article  Google Scholar 

  • Chiarella, C., Iori, G., & Perelló, J. (2009). The impact of heterogeneous trading rules on the limit order book and order flows. Journal of Economic Dynamics and Control, 33(3), 525–537.

    Article  Google Scholar 

  • Cont, R. (2001). Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance, 1, 223–236.

    Article  Google Scholar 

  • Cont, R. (2005). Chapter 7 - Agent-Based Models for Market Impact and Volatility. A Kirman and G Teyssiere: Long memory in economics, Springer.

  • da Costa Pereira, C., Mauri, A., & Tettamanzi, A. G. (2009). Cognitive-agent-based modeling of a financial market. In 2009 IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology (vol. 2, pp. 20–27). IEEE.

  • Cristelli, M. (2014). Complexity in Financial Markets. Springer.

  • Dayan, P., & Daw, N. D. (2008). Decision theory, reinforcement learning, and the brain. Cognitive, Affective, and Behavioral Neuroscience, 8(4), 429–453.

    Article  Google Scholar 

  • Deng, Y., Bao, F., Kong, Y., Ren, Z., & Dai, Q. (2017). Deep direct reinforcement learning for financial signal representation and trading. IEEE Transactions on Neural Networks and Learning Systems, 28(3), 653–664.

    Article  Google Scholar 

  • Dodonova, A., & Khoroshilov, Y. (2018). Private information in futures markets: An experimental study. Managerial and Decision Economics, 39, 65–70.

    Article  Google Scholar 

  • Duncan, K., Doll, B. B., Daw, N. D., & Shohamy, D. (2018). More than the sum of its parts: A role for the hippocampus in configural reinforcement learning. Neuron, 98, 645–657.

    Article  Google Scholar 

  • Eickhoff, S. B., Yeo, B. T. T., & Genon, S. (2018). Imaging-based parcellations of the human brain. Nature Reviews Neuroscience, 19, 672–686.

    Article  Google Scholar 

  • Erev, I., Roth, E., & A. (2014). Maximization, learning and economic behaviour. PNAS, 111, 10818–10825.

    Article  Google Scholar 

  • Fama, E. (1970). Efficient capital markets: A review of theory and empirical work. Journal of Finance, 25, 383–417.

    Article  Google Scholar 

  • Farmer, J. D., & Foley, D. (2009). The economy needs agent-based modelling. Nature, 460(7256), 685–686. https://doi.org/10.1073/pnas.0409157102

    Article  Google Scholar 

  • Farmer, J. D., Patelli, P., & Zovko, I. I. (2005). The predictive power of zero intelligence in financial markets. Proceedings of the National Academy of Sciences of the United States of America, 102(6), 2254–2259. https://doi.org/10.1073/pnas.0409157102

    Article  Google Scholar 

  • Franke, R., & Westerhoff, F. (2011). Structural stochastic volatility in asset pricing dynamics: Estimation and model contest. BERG Working Paper Series on Government and Growth 78.

  • Frydman, C., & Camerer, C. F. (2016). The psychology and neuroscience of financial decision making. Trends in Cognitive Sciences, 20, 661–675.

    Article  Google Scholar 

  • Ganesh, S., Vadori, N., Xu, M., Zheng, H., Reddy, P., & Veloso, M. (2019). Reinforcement learning for market making in a multi-agent dealer market. arXiv:1911.05892.

  • Gao, J., Buldyrev, S. V., Stanley, H. E., & Havlin, S. (2012). Networks formed from interdependent networks. Nature physics, 8, 40–48.

    Article  Google Scholar 

  • Gode, D., & Sunder, S. (1993). Allocative efficiency of markets with zero-intelligence traders: Market as a partial substitute for individual rationality. Journal of Political Economy, 101(1), 119–137.

    Article  Google Scholar 

  • Greene, W. H. (2017). Econometric Analysis (8th ed.). Pearson.

  • Grossman, S. J., & Stiglitz, J. E. (1980). On the impossibility of informationally efficient markets. The American Economic Review, 70(3), 393–408.

    Google Scholar 

  • Gualdi, S., Tarzia, M., Zamponi, F., & Bouchaud, J. P. (2015). Tipping points in macroeconomic agent-based models. Journal of Economic Dynamics and Control, 50, 29–61.

    Article  Google Scholar 

  • Hanson, T. A. (2011). The effects of high frequency traders in a simulated market. In: Midwest Finance Association 2012 Annual Meetings Paper.

  • Hardiman, S. J., Bercot, N., & Bouchaud, J. P. (2013). Critical reflexivity in financial markets: a hawkes process analysis. arXiv:1302.1405.

  • Hu, Y. J., & Lin, S. J. (2019). Deep reinforcement learning for optimizing portfolio management. In 2019 amity international conference on artificial intelligence.

  • Huang, W., Lehalle, C. A., & Rosenbaum, M. (2015). Simulating and analyzing order book data: The queue-reactive model. Journal of the American Statistical Association, 110, 509.

    Article  Google Scholar 

  • Kendall, G., Su, Y. (2003). The co-evolution of trading strategies in a multi-agent based simulated stock market through the integration of individual learning and social learning. In Proceedings of IEEE (pp. 2298–2305).

  • Lanctot, M., Zambaldi, V., Gruslys, A., Lazaridou, A., Tuyls, K., Perolat, J., et al. (2017). A unified game-theoretic approach to multiagent reinforcement learning. Advances in Neural Information Processing Systems, 30(NIPS 2017), 4190–4203.

    Google Scholar 

  • Leal, S. J., Napoletano, M., Roventini, A., & Fagiolo, G. (2016). Rock around the clock: An agent-based model of low-and high-frequency trading. Journal of Evolutionary Economics, 26(1), 49–76.

    Article  Google Scholar 

  • LeBaron, B. (2002). Building the santa fe artificial stock market. Physica A pp. 1–20.

  • Lee, D., Seo, H., & Jung, M. W. (2012). Neural basis of reinforcement learning and decision making. Annual Review of Neuroscience, 35(1), 287–308. https://doi.org/10.1146/annurev-neuro-062111-150512

    Article  Google Scholar 

  • Lee, J. W., Park, J., Jangmin, O., Lee, J., & Hong, E. (2007). A multiagent approach to \( q \)-learning for daily stock trading. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 37(6), 864–877.

    Article  Google Scholar 

  • Lefebvre, G., Lebreton, M., Meyniel, F., Bourgeois-Gironde, S., & Palminteri, S. (2017). Behavioural and neural characterization of optimistic reinforcement learning. Nature Human Behaviour, 1(4), 1–9.

    Article  Google Scholar 

  • Lipski, J., & Kutner, R. (2013). Agent-based stock market model with endogenous agents’ impact. arXiv:1310.0762.

  • Lussange, J., Belianin, A., Bourgeois-Gironde, S., & Gutkin, B. (2020). Learning and cognition in financial markets: A paradigm shift for agent-based models. In Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1252).

  • Lussange, J., Lazarevich, I., Bourgeois-Gironde, S., Palminteri, S., & Gutkin, B. (2020). Modelling stock markets by multi-agent reinforcement learning. Computational Economics, 57, 113–147.

    Article  Google Scholar 

  • Lux, T., & Marchesi, M. (1999). Scaling and criticality in a stochastic multi-agent model of a financial market. Nature, 397(6719), 498–500.

    Article  Google Scholar 

  • Maslov, S. (2000). Simple model of a limit order-driven market. Physica A: Statistical Mechanics and its Applications, 278(3–4), 571–578.

    Article  Google Scholar 

  • Momennejad, I., Russek, E., Cheong, J., Botvinick, M., Daw, N. D., & Gershman, S. J. (2017). The successor representation in human reinforcement learning. Nature Human Behavior, 1, 680–692.

    Article  Google Scholar 

  • Mota Navarro, R., & Larralde, H. (2017). A detailed heterogeneous agent model for a single asset financial market with trading via an order book. PloS one, 12(2), e0170766.

    Article  Google Scholar 

  • Murray, M. P. (1994). A drunk and her dog: An illustration of cointegration and error correction. The American Statistician, 48(1), 37–39.

    Google Scholar 

  • Naik, P. K., Gupta, R., & Padhi, P. (2018). The relationship between stock market volatility and trading volume: Evidence from South Africa. The Journal of Developing Areas, 52(1), 99–114.

    Article  Google Scholar 

  • Neuneier, R. (1997). Enhancing q-learning for optimal asset allocation. In Proc. of the 10th International Conference on Neural Information Processing Systems.

  • Palminteri, S., Khamassi, M., Joffily, M., & Coricelli, G. (2015). Contextual modulation of value signals in reward and punishment learning. Nature communications, 6, 1–14.

    Article  Google Scholar 

  • Platt, D., & Gebbie, T. (2018). Can agent-based models probe market microstructure? Physica A: Statistical Mechanics and its Applications, 503, 1092–1106.

    Article  Google Scholar 

  • Potters, M., & Bouchaud, J. P. (2001). More stylized facts of financial markets: Leverage effect and downside correlations. Physica A, 299, 60–70.

    Article  Google Scholar 

  • Preis, T., Golke, S., Paul, W., & Schneider, J. J. (2006). Multi-agent-based order book model of financial markets. EPL (Europhysics Letters), 75(3), 510.

    Article  Google Scholar 

  • Ross, S. (1973). The economic theory of agency: The principal’s problem. American Economic Review, 63(2), 134–39.

    Google Scholar 

  • Silver, D., Hubert, T., Schrittwieser, J., Antonoglou, I., Lai, M., Guez, A., Lanctot, M., Sifre, L., Kumaran, D., Graepel, T., Lillicrap, T., Simonyan, K., & Hassabis, D. (2018). A general reinforcement learning algorithm that masters chess, shogi and go through self-play. Science, 362(6419), 1140–1144.

    Article  Google Scholar 

  • Sirignano, J., & Cont, R. (2019). Universal features of price formation in financial markets: Perspectives from deep learning. Quantitative Finance, 19(9), 1449–1459.

    Article  Google Scholar 

  • Sornette, D. (2014). Physics and financial economics (1776–2014): puzzles, ising and agent-based models. Reports on Progress in Physics, 77(6), 062001.

    Article  Google Scholar 

  • Spooner, T., Fearnley, J., Savani, R., & Koukorinis, A. (2018). Market making via reinforcement learning. In Proceedings of the 17th AAMAS.

  • Sutton, R., & Barto, A. (2018). Reinforcement Learning, second edition: An Introduction. Bradford Books

  • Szepesvari, C. (2010). Algorithms for Reinforcement Learning. Morgan and Claypool Publishers.

    Book  Google Scholar 

  • Way, E., & Wellman, M. P. (2013). Latency arbitrage, market fragmentation, and efficiency: a two-market model. In Proceedings of the fourteenth ACM conference on Electronic commerce (pp. 855–872).

  • Westerhoff, F. H. (2008). The use of agent-based financial market models to test the effectiveness of regulatory policies. Jahrbucher Fur Nationalokonomie Und Statistik, 228(2), 195. https://doi.org/10.1515/jbnst-2008-2-305

    Article  Google Scholar 

  • Wiering, M., & van Otterlo, M. (2012). Reinforcement Learning: State-of-the-Art. Springer.

    Book  Google Scholar 

  • Xu, H. C., Zhang, W., Xiong, X., & Zhou, W. X. (2014). An agent-based computational model for china’s stock market and stock index futures market. Mathematical Problems in Engineering, 2014, 563912.

    Google Scholar 

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Acknowledgements

We graciously acknowledge this work was supported by the HSE Basic Research Program and the Russian Academic Excellence Project “5-100” and CNRS PRC nr. 151199, and received support from FrontCog ANR-17-EURE-0017. Also, S.P. is supported by an ATIP-Avenir grant (R16069JS), the Programme Emergence(s) de la Ville de Paris, the Fondation Fyssen, the Fondation Schlumberger pour l’Education et la Recherche and the IRESP (project EPELNOR).

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Lussange, J., Vrizzi, S., Bourgeois-Gironde, S. et al. Stock Price Formation: Precepts from a Multi-Agent Reinforcement Learning Model. Comput Econ 61, 1523–1544 (2023). https://doi.org/10.1007/s10614-022-10249-3

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