Abstract
In this paper, we propose a generalization of the classical ”martingale-plus-noise” model for prices on a high-frequency level. In our framework, observed prices are driven by market microstructure noise and the prevailing discrepancy between observed prices and efficient prices. The speed by which observed prices adjust to the ”mis-pricing” component is governed by a parameter which naturally measures the price efficiency on the market. The framework provides a structural approach for the linkage between observed prices and efficient prices and the role of feedback effects in trading. It allows to capture a wide range of stochastic behavior in observed micro prices and captures the classical ”martingale plus i.i.d. noise" framework as a special case.
We illustrate that the variance of the mis-pricing components is naturally linked to a measure of the market efficiency and demonstrate that its interplay with the signal-to-noise ratio determines two major regimes in the market: when the signal-to-noise ratio is low relative to the variance of mis-pricing, observed returns become negatively autocorrelated and observed prices tend to revert towards efficient prices. In the opposite case, observed returns become positively correlated and observed prices reveal local trends in line with momentum behavior. By locally estimating the model based on NASDAQ limit order book data, we empirically identify the presence of these two regimes in terms of the model parameters and show that they are in line with autocorrelations in observed returns.
We moreover show that the two regimes imply different behavior of realized volatility estimators sampled on high frequencies. While in one regime resulting volatility-signature plots are upward sloped for increasing sampling frequencies, a reverse pattern prevails in the other. We provide empirical evidence on local volatility-signature plots and demonstrate substantial time variations of the corresponding shapes. Our results therefore provide new insights for high-frequency based volatility estimation, provide new channels for the construction of improved estimators and establish a direct link to underlying market microstructure literature.
We illustrate that the variance of the mis-pricing components is naturally linked to a measure of the market efficiency and demonstrate that its interplay with the signal-to-noise ratio determines two major regimes in the market: when the signal-to-noise ratio is low relative to the variance of mis-pricing, observed returns become negatively autocorrelated and observed prices tend to revert towards efficient prices. In the opposite case, observed returns become positively correlated and observed prices reveal local trends in line with momentum behavior. By locally estimating the model based on NASDAQ limit order book data, we empirically identify the presence of these two regimes in terms of the model parameters and show that they are in line with autocorrelations in observed returns.
We moreover show that the two regimes imply different behavior of realized volatility estimators sampled on high frequencies. While in one regime resulting volatility-signature plots are upward sloped for increasing sampling frequencies, a reverse pattern prevails in the other. We provide empirical evidence on local volatility-signature plots and demonstrate substantial time variations of the corresponding shapes. Our results therefore provide new insights for high-frequency based volatility estimation, provide new channels for the construction of improved estimators and establish a direct link to underlying market microstructure literature.
| Original language | English (US) |
|---|---|
| Number of pages | 34 |
| State | Published - Jan 10 2016 |
Keywords
- High-frequency data
- Volatility estimation
- Market microstructure noise
- Trade reversals