Commonalities in the Order Book

TLDR: In this article, the authors used data from one of the most important European stock markets and showed that, in line with predictions from theoretical market microstructure, a small number of latent factors captures most of the variation in stock specific order books.

Abstract: More and more trading venues throughout the world operate as open order book markets. In those exchanges, liquidity is supplied voluntarily by market participants who provide an inflow of limit buy and sell orders. Non-executed orders constitute the limit order book which consists of distinct, sorted limit price-depth pairs. This paper uses data from one of the most important European stock markets and shows that, in line with predictions from theoretical market microstructure, a small number of latent factors captures most of the variation in stock specific order books. We show that these order book commonalities are much stronger than liquidity commonality across stocks. The result that bid and ask side as well as the visible and hidden parts of the order book exhibit quite specific dynamics is interpreted as evidence that open order book markets attract a heterogeneous trader population in terms of asset valuations and impatience. The paper also shows that the information share attributable to the extracted factors with respect to the long run evolution of the asset price is non-negligible. In other words, shifts and rotations of the order book carry informational content. The information shares are considerably different across stocks. While for the group of most actively traded stocks (which are also the biggest in terms of market capitalization) we estimate an average information share attributable to the extracted factors of about 5 percent, the number doubles for the group of least frequently traded stocks. On the other hand, the hidden part of the book does not carry economically significant informational content.

Figures

Table V: Factors and volatility

Figure 6: Diurnal variation of the first two principal components for the visible ask side (top of figure) and visible bid side (bottom of figure). Averages for the 30 stocks in our sample.The dotted line are the confidence bands at 95%. 41

Figure 2: Autocorrelograms for v-euros ask price impacts (500 lags), complete book, BAYER. One trading day has 102 observations.

Table II: Fraction of the variance of the price impacts explained by given frequency bands

Figure 5: Simulations of the ask side of the book (Bayer stock) when the first and second principal components are individually increased (X2, X4) or decreased (X0.5, X0.25). The initial state is characterized by X1. From top to bottom, the panels present successively the individual effects of the increase/decrease of the first and second principal components. 40

Table III: Correlations between price impact series

Frequently asked questions

Q1. What have the authors contributed in "Département des sciences économiques de l'université catholique de louvain commonalities in the order book" ?

In this paper the authors provide empirical evidence that indeed a small number of latent factors, two for each side of the book, capture most of the variation in the price-depth pairs. 

Q2. What have the authors stated for future works in "Département des sciences économiques de l'université catholique de louvain commonalities in the order book" ?

Secondly, in a cross section framework, the authors run regressions where the stock specific explanatory powers of the shift and rotation factor are regressed on a stock specific measure of the informational content of the order flow and a transaction costs measure that is purged of informational effects. 

Q3. What is the effect of a properly constructed order imbalance indicator?

If the rotation factor qualifies as a liquidity factor then the authors would expect a positive effect of a properly constructed order imbalance indicator. 

Q4. How many principal components are needed in the visible-hidden PCA?

Whilst in the latter application two principal components (identified as shift and rotation factor) achieved a cumulative R2 of about 0.92, the cumulative explanatory power of the first two principal components in the joint visible-hidden PCA is only .77 (average across stocks). 

Q5. What is the importance of the disequilibrium between buyers and sellers?

19Seppi (1997) stresses the importance of the disequilibrium between buyers and sellers in that a larger proportion of buy than sell trades increase the likelihood of execution for sell limit orders. 

Q6. What is the first application of PCA to order book data?

Since PCA requires standardized stationary data input (otherwise the variables with largest sample variance tend to receive too much weight) 8Gouriéroux, Le Fol, and Meyer (1998) present the first application of PCA to order book data of French Euronext-traded stocks. 

Q7. What is the empirical application of Xetra?

The empirical application deals with the Xetra trading system, which is a pure automated auction market similar to Euronext or the Hong Kong stock exchange. 

Q8. What is the explanatory power of the first n principal components?

The explanatory power (referred to as cumulative R2) of the first n principal components F1, F2, . . . , Fn can be computed by dividing the sum of the n first eigenvalues by the total sum of all N eigenvalues. 

Q9. What are the regressors of the shift and rotation factors?

For this purpose the authors estimate regressions where the extracted shift and rotation factors serve as dependent variables and indicators suggested by microstructure theory as regressors. 

Q10. What is the unit price at(v) of a buy of size v at time?

The available pre-trade liquidity of the book can be characterized by the unit price for selling v shares at time t:bt(v) = ∑k bk,tvk,t v(1)where v is the volume executed at k different unique bid prices bk,t with corresponding volumes vk,t standing in the limit order book at time t. The unit price at(v) of a buy of size v at time t can be computed analogously.