The Time-Adjusted Micro-Price and the Relevance of Deeper Limit Order Book Levels

A key variable for the applied trading strategies and for market microstructure research in general is the estimation of the true security price which is by nature a continuous measure. In previous research, the true price is predominantly approximated by the mid-price or the quantity-weighted mid-price. However, both price measures have weaknesses that limit their applications. The simple mid-price, for example, is artificially discretized by the tick size and does not have desirable properties like being a martingale process. Although these problems do not apply to the quantity-weighted mid-price, this measure can reflect incorrect price movements in the event of changes in the bid-ask spread. The microprice by Stoikov (2018) addresses all these shortcomings and takes into account quantity imbalance and bid-ask spread by means of a Markov chain. Furthermore, it can also be extended by accounting for other variables. The goal of this thesis is to replicate the methodology defined by Stoikov and to extend the microprice measure by different variables. On the one hand, the age of the corresponding buy and sell orders shall be considered, on the other hand, lower levels of the limit order book shall be taken into account. For this purpose, the student was provided with historical limit order book data of various DAX40 stocks. While the descriptive statistics suggest a weak relation between the future mid-price and the time imbalance, the results do not provide evidence that the time imbalance or deeper limit order book levels are significantly relevant for future mid-price changes by means of the microprice. However, contrary to the findings of Stoikov (2018), the results suggest that for most forecasting horizons the microprice is not a better predictor of the future mid-price than the actual mid-price or the quantity-weighted mid-price.