Order Flows and LOB Evolution

Most traditional execution models in the literature decompose price impact into instantaneous and permanent impacts. The former (discussed in the previous sec- tion) models impact only on the current transaction price, and usually carries the assumptions that the LOB recovers infinitely fast to its previous state. The latter captures the impact on the mid-price that persists and affects trading in the future. An alternative approach applied in so-called resilience models [2, 32, 3] instead as- sumes transient impact. That is, the LOB has some general shape, market orders arrive and impact the mid-price by consuming a portion of the LOB and finally limit orders “refill” over time, often exponentially. In reality, following a market execution, the LOB response varies widely, at times bouncing back immediately in a resilient fashion, while other times falling through and retreating.

Figure 3.2 illustrates the evolution of the LOB for TEVA on 2/18/2011 over a period of 90 seconds. To visualize the book, we focus on the top 2 queues with

volumes vA

1(t) and v1B(t) (left axis). A vertical line represents the jump caused by an

arriving order and horizontal lines represent periods of inactivity at each respective queue. Limit additions and cancellations and market orders (orange) are plotted event-by-event so that the mechanics and sequence of order arrivals are more clear. The right axis corresponds to the mid price (upper lines) with dotted vertical lines marking a change in bid- or ask-price.

● 0 50 100 150 200 0 1000 2000 3000 4000 5000 6000 Event V olume ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● _51.60 51.65 51.70 51.75 Pr ice

Figure 3.2: Best bid/ask queues vj₁(t) for TEVA along with bid/ask price pj₁(t) (top). Data taken

from a 90 second window beginning at 2:30pm on 2/18/2011. Cancellations exceed additions at the best bid. Limit orders are in red and blue depending on side, market executions are orange.

One key element that is showcased in Figure 3.2 is the interaction between limit and market orders. We observe several typical “regimes”, for example periods where market orders are counteracted with added limit orders (so that vj₁(t) stays roughly constant over time), and other periods where market orders are accompanied primar-

ily by LO cancellations, creating a strong negative trend in v₁j(t). The latter situation would correspond to scarce liquidity, as the book is “retreating” along with executed trades. In contrast, in a deep or resilient market, executed orders do not impact the book which bounces back through fresh LO. Visually, one can imagine in Figure 3.2, that excluding market orders, the drift of the queue size at the bid/ask would trend positively through time. Scarce liquidity on the ask (bid) side would be character- ized by the alternative, either negative drift or near zero-drift combined with a high quantity of buy (sell) executions.

The microstructure behavior in Figure 3.2 is on the short time-scale and can be analyzed directly using queue-theoretic methods found in [44, 18, 35]. In that context, factors such as static volume imbalance, queue priority and sign of last market orders are the main drivers. For example, Huang et al. [35] model limit order, cancellation and market order arrival rates as a function of the queue sizes v_ij(t). Under this Markovian assumption tractable formulas can be often be computed for interesting quantities such as the probability of move up or down in the mid-price, but the historical order flow is ignored. Here, we aim to lift these features to a mesoscopic time-scale by documenting and modeling some of the persistent behavior of book liquidity/resilience that are driven by order flows and revealed on the minutes-scale. Figure 3.3 nicely illustrates this point, albeit with a very extreme example. On the July 12, 2012, four large cap US stocks exhibited an unusual trading pattern;

heavy buying following by heavy selling in a predictible fashion at 30 minute inter- vals. One expects that LOB volume imbalance V I(t) should be positively correlated with price movement. This is typically the case. Here we see the opposite is true: As the price moves higher (respectively, lower) there is more depth at the best ask (bid). So while the static look indicates plentiful liquidity, market maker actions, ap- parently responding to the incoming order flow, leads to significant price slippage for the aggressive buyers/sellers. In their research note [40] Lehalle et al. conclude that one likely cause of the very unusual trading behavior was a derivative hedging strat- egy that entirely ignored common knowledge about market microstructure. For our purposes, the event is a clear example of weak LOB resilience as liquidity providers anticipate 1-sided MOF.

Figure 3.3: Plot taken from Lehalle et al. [40]. Stock price P (t) for Coca-Cola and LOB volume imbalance V I(t) at the touch aggregated over 5 minute time bars (green/black).