英文标题：
《Dynamical Models of Stock Prices Based on Technical Trading Rules Part
II: Analysis of the Models》
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作者：
Li-Xin Wang
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最新提交年份：
2016
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英文摘要：
In Part II of this paper, we concentrate our analysis on the price dynamical model with the moving average rules developed in Part I of this paper. By decomposing the excessive demand function, we reveal that it is the interplay between trend-following and contrarian actions that generates the price chaos, and give parameter ranges for the price series to change from divergence to chaos and to oscillation. We prove that the price dynamical model has an infinite number of equilibrium points but all these equilibrium points are unstable. We demonstrate the short-term predictability of the return volatility and derive the detailed formula of the Lyapunov exponent as function of the model parameters. We show that although the price is chaotic, the volatility converges to some constant very quickly at the rate of the Lyapunov exponent. We extract the formula relating the converged volatility to the model parameters based on Monte-Carlo simulations. We explore the circumstances under which the returns show independency and illustrate in details how the independency index changes with the model parameters. Finally, we plot the strange attractor and return distribution of the chaotic price model to illustrate the complex structure and fat-tailed distribution of the returns.
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中文摘要：
在本文的第二部分中，我们集中分析了价格动态模型和本文第一部分中发展的移动平均规则。通过对过度需求函数的分解，我们揭示了正是趋势跟踪和反转行为之间的相互作用产生了价格混沌，并给出了价格序列从发散到混沌再到振荡的参数范围。我们证明了价格动态模型有无穷多个平衡点，但所有这些平衡点都是不稳定的。我们证明了收益率波动率的短期可预测性，并推导了作为模型参数函数的李雅普诺夫指数的详细公式。我们发现，虽然价格是混沌的，但波动率以李雅普诺夫指数的速度很快收敛到某个常数。基于蒙特卡罗模拟，我们提取了收敛波动率与模型参数之间的关系式。我们探讨了收益率表现出独立性的情况，并详细说明了独立性指数如何随模型参数而变化。最后，我们绘制了混沌价格模型的奇怪吸引子和收益分布图，以说明收益的复杂结构和厚尾分布。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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一级分类：Computer Science 计算机科学
二级分类：Computational Engineering, Finance, and Science 计算工程、金融和科学
分类描述：Covers applications of computer science to the mathematical modeling of complex systems in the fields of science, engineering, and finance. Papers here are interdisciplinary and applications-oriented, focusing on techniques and tools that enable challenging computational simulations to be performed, for which the use of supercomputers or distributed computing platforms is often required. Includes material in ACM Subject Classes J.2, J.3, and J.4 (economics).
涵盖了计算机科学在科学、工程和金融领域复杂系统的数学建模中的应用。这里的论文是跨学科和面向应用的，集中在技术和工具，使挑战性的计算模拟能够执行，其中往往需要使用超级计算机或分布式计算平台。包括ACM学科课程J.2、J.3和J.4（经济学）中的材料。
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一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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