In recent years, researchers analyzed the historical data from the financial markets. They found that the statistical result is different from the classical financial theories, models, and methods. The difference is challenging the three hypotheses which are rational people hypothesis, efficient market hypothesis and random walk hypothesis. We need new perspective and tools to re-study the financial market as a complex system. A cellular automata based heterogeneous financial market model is proposed in this categories which dissertation. In this model, the market participant id divided in to two is the fundamentalists and chartists. A learn rules is used to make sure all the market participant can convert in these two categories. The method emulates the interact behaviors between the market participants, and emulates the overall market behavior. The author analyzes the randomness sources, mean-reverting property, bubble happen and bust, and stationary of this model. The author analyzes the relationships between cellular automata based heterogeneous financial market model and the Ornstein-Uhlenbeck model and GARCH models. The data simulated by the financial market model is fit the characteristics such as the fat tail of return's distribution, negative skewness, relationship between return and trading volume, the randomness of volatility, and volatility cluster, which the classical theory is failed to explain. How to add more heterogeneity into the model is discussed in this dissertation. In this dissertation, by using the cellular automata as a tool, an option pricing model and a heterogeneous financial market model are proposed. The result of the option pricing model is close to the result calculated by the formula. The simulation of heterogeneous financial market model can explain many phenomenons which can not be explained by the classical theory, such as the fat-tail of return and the bubble happen and bust. The author also preliminary designs the financial market model based on the asynchronous cellular automata. These models and conclusions indicate that cellular automata have a ability to show the randomness of the financial markets and simulate the behaves of the participants in the financial maket.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 3) |
| DOI | 10.11648/j.sjams.20150303.18 |
| Page(s) | 153-159 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2015. Published by Science Publishing Group |
Cellular Automaton, Financial Market, Heterogeneous, Simulation
| [1] | Gao Y Beni G Price Fluctuations in Market Model with Heterogeneous Trading Strategies. Proceedings of tha 4th IASTED: Financial Engineering and Application, Berkeley CA, 2007. |
| [2] | Gao Y, Beni G. Model of Heterogeneous Market wiih Intrinsic Randomness. International Conference on Computational Intelligence in Economics & Finance, Salt Lake City, UT, 2007. |
| [3] | Barndorff-Nielsen O E, Shephard N. Non-Gaussian Ornstein Uhlenbeck-based Models and Some of Their Uses in Financial Economics [J]. Journal of the Royal Statistical Society, Series B, Vo1. 63(2), 2001, 167-241. |
| [4] | Engle R E. Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation [3]. Econometrics, Vo1.50, 1982, 987-1007. |
| [5] | Bollerslev T. Generalized Autoregressive Conditional Heteroskedasticity [J]. Journal of Econometrics, Vol. 3(1), 1986, 307-328. |
| [6] | Malkiel B G. The Efficient Market Hypothesis and Its Critics [J]. The Journal of Economic. Perspectives, Vo1. 17(1), 2003, 59-82. |
| [7] | Lux T. The Socio-economic Dynamics of Speculative Markets: Interacting Agents, Chaos, and the Fat Tails of Return Distributions [J]. Journal of Economic Behavior and Organization, Vo1.33 (2), 1998, 143-165. |
| [8] | Chairella C, Dieci R, Gardini L. Asset Price Dynamic in a Financial Market with Fundamentalist and Chartists [J]. Discrete Dynamics in Nature and Society, Vol. 6(2), 2001, 69-99. |
| [9] | Horst U,. Financial Price Fluctuations in a Stock Market Model with Many Interacting. Agents [J]. Economic Theory, Vo1. 25(4), 2005, 917-932. |
| [10] | Follmer H, Horst U, Kirman A. Equilibria in Financial Markets with Heterogeneous. Agents: A Probabilistic Perspective [J], Journal of Mathematical Economics, Vo1. 41(1-2), 2005, 123-155. |
| [11] | Uhlenbeck G E, Ornstein L S. On the Theory of Brownian Motion [J]. Physical Review. Letters, Vo1.36, 1930, 823-841. |
| [12] | Feller W. An Introduction to Probability Theory and its Applications [M], Wiley, 1958. |
| [13] | Larralde H. Statstical Properties of a Discrete Version of the Ornstein- Uhlenbeck, Process [J]. Physical Review E, Vo1.69, 2004, 027102. |
| [14] | Vasicek O A. An Equilibrium Characterization of Tenn Structure [J]. Journal of Financial, Economics, Vo1.5, 1977, 177-188. |
APA Style
Hong Zhang, Li Zhou, Yifan Yang, Lu Qiu. (2015). Simulation of Heterogeneous Financial Market Model Based on Cellular Automaton. Science Journal of Applied Mathematics and Statistics, 3(3), 153-159. https://doi.org/10.11648/j.sjams.20150303.18
ACS Style
Hong Zhang; Li Zhou; Yifan Yang; Lu Qiu. Simulation of Heterogeneous Financial Market Model Based on Cellular Automaton. Sci. J. Appl. Math. Stat. 2015, 3(3), 153-159. doi: 10.11648/j.sjams.20150303.18
AMA Style
Hong Zhang, Li Zhou, Yifan Yang, Lu Qiu. Simulation of Heterogeneous Financial Market Model Based on Cellular Automaton. Sci J Appl Math Stat. 2015;3(3):153-159. doi: 10.11648/j.sjams.20150303.18
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Download@article{10.11648/j.sjams.20150303.18,
author = {Hong Zhang and Li Zhou and Yifan Yang and Lu Qiu},
title = {Simulation of Heterogeneous Financial Market Model Based on Cellular Automaton},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {3},
number = {3},
pages = {153-159},
doi = {10.11648/j.sjams.20150303.18},
url = {https://doi.org/10.11648/j.sjams.20150303.18},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150303.18},
abstract = {In recent years, researchers analyzed the historical data from the financial markets. They found that the statistical result is different from the classical financial theories, models, and methods. The difference is challenging the three hypotheses which are rational people hypothesis, efficient market hypothesis and random walk hypothesis. We need new perspective and tools to re-study the financial market as a complex system. A cellular automata based heterogeneous financial market model is proposed in this categories which dissertation. In this model, the market participant id divided in to two is the fundamentalists and chartists. A learn rules is used to make sure all the market participant can convert in these two categories. The method emulates the interact behaviors between the market participants, and emulates the overall market behavior. The author analyzes the randomness sources, mean-reverting property, bubble happen and bust, and stationary of this model. The author analyzes the relationships between cellular automata based heterogeneous financial market model and the Ornstein-Uhlenbeck model and GARCH models. The data simulated by the financial market model is fit the characteristics such as the fat tail of return's distribution, negative skewness, relationship between return and trading volume, the randomness of volatility, and volatility cluster, which the classical theory is failed to explain. How to add more heterogeneity into the model is discussed in this dissertation. In this dissertation, by using the cellular automata as a tool, an option pricing model and a heterogeneous financial market model are proposed. The result of the option pricing model is close to the result calculated by the formula. The simulation of heterogeneous financial market model can explain many phenomenons which can not be explained by the classical theory, such as the fat-tail of return and the bubble happen and bust. The author also preliminary designs the financial market model based on the asynchronous cellular automata. These models and conclusions indicate that cellular automata have a ability to show the randomness of the financial markets and simulate the behaves of the participants in the financial maket.},
year = {2015}
}
TY - JOUR T1 - Simulation of Heterogeneous Financial Market Model Based on Cellular Automaton AU - Hong Zhang AU - Li Zhou AU - Yifan Yang AU - Lu Qiu Y1 - 2015/06/01 PY - 2015 N1 - https://doi.org/10.11648/j.sjams.20150303.18 DO - 10.11648/j.sjams.20150303.18 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 153 EP - 159 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20150303.18 AB - In recent years, researchers analyzed the historical data from the financial markets. They found that the statistical result is different from the classical financial theories, models, and methods. The difference is challenging the three hypotheses which are rational people hypothesis, efficient market hypothesis and random walk hypothesis. We need new perspective and tools to re-study the financial market as a complex system. A cellular automata based heterogeneous financial market model is proposed in this categories which dissertation. In this model, the market participant id divided in to two is the fundamentalists and chartists. A learn rules is used to make sure all the market participant can convert in these two categories. The method emulates the interact behaviors between the market participants, and emulates the overall market behavior. The author analyzes the randomness sources, mean-reverting property, bubble happen and bust, and stationary of this model. The author analyzes the relationships between cellular automata based heterogeneous financial market model and the Ornstein-Uhlenbeck model and GARCH models. The data simulated by the financial market model is fit the characteristics such as the fat tail of return's distribution, negative skewness, relationship between return and trading volume, the randomness of volatility, and volatility cluster, which the classical theory is failed to explain. How to add more heterogeneity into the model is discussed in this dissertation. In this dissertation, by using the cellular automata as a tool, an option pricing model and a heterogeneous financial market model are proposed. The result of the option pricing model is close to the result calculated by the formula. The simulation of heterogeneous financial market model can explain many phenomenons which can not be explained by the classical theory, such as the fat-tail of return and the bubble happen and bust. The author also preliminary designs the financial market model based on the asynchronous cellular automata. These models and conclusions indicate that cellular automata have a ability to show the randomness of the financial markets and simulate the behaves of the participants in the financial maket. VL - 3 IS - 3 ER -
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