单一市场内趋势与反转的隐状态模型
文章 arXiv papers · 作者: Kuang-Ting Chen
总结
本文提出一个用于刻画价格非效率的双变量隐马尔可夫时间序列模型，将分析拓展至几何布朗运动之外。其中一个变量——合理价格——不可观测。在模型最简单的形式中，本文使用路径积分和格林函数方法分析市场价格相对于这一潜在价值的表现。
当合理价格的对数波动率高于市场价格的对数波动率时，模型预测趋势跟踪行为；反之则预测均值回归。模型还令风险溢价与市场价格和其指数移动平均线之间的差值成正比，从理论上解释过去价格如何影响未来价格。作者介绍了参数估计方法：在傅里叶空间中积分消去隐藏价格，采用最大似然估计，随后考察近期S&P 500数据。所提供的描述没有拟合统计或预测表现证据，因此无法据此判断该模型是否适用于交易，或能否推广至该指数分析之外。
核心观点
- 潜在合理价格与可观测市场价格构成了一个用于刻画价格非效率的双变量模型。
- 模型根据两个价格过程的相对波动率预测趋势或反转。
- 模型的风险溢价与市场价格和其指数移动平均线之间的差值相关。
- 参数估计通过傅里叶空间积分消去隐藏价格。
- 本文考察S&P 500数据，但描述中没有报告拟合或交易表现指标。
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# Modeling Market Inefficiencies within a Single Instrument # Modeling Market Inefficiencies within a Single Instrument In this paper, we propose a minimal model beyond geometric Brownian motion that aims to describe price actions with market inefficiency. From simple financial theory considerations, we arrive at a simple two-variable hidden Markovian time series model, with one of the variable entirely unobserved. Then, we analyze the simplest version of the model, using path integral and Green's function techniques from physics. We show that in this model, the inefficient market price is trend-following when the standard deviation of the log reasonable price ($σ$) is larger than that of the log market price ($σ'$), and mean-reversing when it is smaller. The risk premium is proportional to the difference between the current market price and the exponential moving average (EMA) of the past prices. This model thus provides a theoretical explanation how the EMA of the past price can directly affect future prices, i.e., the so-called ``Bollinger bands" in technical analyses. We then carry out a maximum likelihood estimate for the model parameters from the observed market price, by integrating out the reasonable price in Fourier space. Finally we analyze recent S\&P500 index data and see to what extent the real world data can be described by this simple model.
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