Abstract

The paper presents a simple agent-based model of the financial market, in which one type of security is traded. There are two assets in the model - the speculative security and money. All agents in the model are players of the same type, their behavior obeys a simple algorithm. An important feature of the model is that the expectations of the future prices are the same for all agents. Agents differ in their investment horizon. Experimentally obtained time series were tested for the presence of well known stylized facts. In particular, the experimental time series show presence of the fat tails effect. On the other hand, the effect of volatility clustering for these time series is not revealed.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 6
Year: 2021

DOI: 10.12732/ijam.v34i6.13

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References

1. [1] B. Mandelbrot, The variation of certain speculative prices, The Journal of Business, 36, No 4 (1963), 394419.
2. [2] R. Cont, Empirical properties of asset returns: stylized facts and statistical issues, Quantitative Finance, 1, No 2 (2001), 223-236.
3. [3] N. Ehrentreich, Agent-based modeling: The Santa Fe Institute artificial stock market model revisited, In: Lecture Notes in Economics and Mathematical Systems, Springer Science & Business Media (2007).
4. [4] J. Campbell, A. Lo, A. MacKinlay, R. Whitelaw, The econometrics of financial markets, In: Macroeconomic Dynamics, Princeton University Press (1997).
5. [5] T. Lux, Stochastic behavioral asset-pricing models and the stylized facts, Handbook of financial markets: Dynamics and evolution, In: Handbooks in Finance (2009), 161-215.
6. [6] S. Cramer, T. Trimborn, Stylized Facts and Agent-Based Modeling, Preprint arXiv:1912.02684 (2019).
7. [7] G. Kim, H. Markowitz, Investment rules, margin and market volatility, Journal of Portfolio Management, 16 (1989), 4552.
8. [8] M. Levy, H. Levy, S. Solomon, A microscopic model of the stock market: Cycles, booms, and crashes, Economics Letters, 45, No 1 (1994), 103111.
9. [9] M. Levy, S. Solomon, Power laws are logarithmic Boltzmann laws, International Journal of Modern Physics C, 7, No 4 (1996), 595601.
10. [10] S. Solomon, M. Levy, Spontaneous scaling emergence in generic stochastic systems, International Journal of Modern Physics C, 7, No 5 (1996), 745751.
11. [11] X. He, K. Li, Heterogeneous beliefs and adaptive behaviour in a continuous-time asset price model, Journal of Economic Dynamics and Control, 36, No 7 (2012), 973987.
12. [12] F. Westerhoff, Multiasset market dynamics, Macroeconomic Dynamics, 8, No 5 (2004), 591616.
13. [13] N. Schmitt, F. Westerhoff, Speculative behavior and the dynamics of interacting stock markets, Journal of Economic Dynamics and Control, 45 (2014), 262288.
14. [14] F.Westerhoff, R. Dieci, The effectiveness of KeynesTobin transaction taxes when heterogeneous agents can trade in different markets: A behavioral finance approach, Journal of Economic Dynamics and Control, 30, No 2 (2006), 293322.
15. [15] R. Dieci, I. Foroni, L. Gardini, X. He, Market Mood, Adaptive Beliefs and Asset Price Dynamics, Chaos, Solutions & Fractals, 29, No 3 (2006), 520-534.
16. [16] M. Lettau, Explaining the facts with adaptive agents: The case of mutual fund flows, Journal of Economic Dynamics and Control, 21, No 7 (1997), 11171147.
17. [17] J. Arifovic, The behavior of the exchange rate in the genetic algorithm and experimental economies, Journal of Political Economy, 104, No 3 (1996), 510541.
18. [18] D. Ladley, Zero intelligence in economics and finance, The Knowledge Engineering Reviw, 27, No 2 (2012), 273-286.
19. [19] W. Brock, C. Hommes, Heterogeneous beliefs and routes to chaos in a simple asset pricing model, Journal of Economic Dynamics and Control, 22, No 8-9 (1998), 12351274.
20. [20] W. Arthur, J. Holland, B. LeBaron, R. Palmer, P. Tayler, Asset pricing under endogenous expectations in an artificial stock market. In: W.B. Arthur, S. Durlauf, D. Lane (Eds.), The Economy as an Evolving Complex System II. Addison-Wesley, Reading, MA (1997), 1544.