A Hidden-State Model of Trends and Reversals Within One Market

Summary

This paper proposes a two-variable hidden Markovian time-series model for price inefficiencies, extending beyond geometric Brownian motion. One variable, the reasonable price, is unobserved. In the simplest form of the model, path-integral and Green’s-function methods are used to analyze how market prices behave relative to that latent value.

The model predicts trend-following behavior when the reasonable-price log volatility exceeds market-price log volatility, and mean reversion when the relationship is reversed. It also makes the risk premium proportional to the gap between the market price and its exponential moving average, offering a theoretical account of how past prices can influence future prices. The authors describe estimating parameters by maximum likelihood while integrating out the hidden price in Fourier space, then examining recent S&P 500 data. The supplied description gives no fit statistics or evidence about predictive performance, so it does not establish whether the model is useful for trading or generalizes beyond that index analysis.

Key ideas

• A latent reasonable price and observed market price form a two-variable model of inefficiency.
• The model predicts trends or reversals depending on the relative volatility of the two price processes.
• Its risk premium is linked to the difference between market price and its exponential moving average.
• Parameter estimation integrates out the hidden price in Fourier space.
• The paper examines S&P 500 data but the description reports no fit or trading-performance metrics.

Tags

# 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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