Interpreting Order Flow Imbalance and Midprice Changes

Summary

The document discusses a worked example from research on price impact, where market sells consume bid depth and limit bid additions replenish it. The response interprets the sequence in ticks: selling 15 shares against depth of 5 removes three levels, while adding 7 bid shares replenishes one full level and part of another. The net share change is negative 8, and the best bid ends one tick below its initial level. This reconciles the displayed price movement with the distinction between the share imbalance and the number of fully crossed price levels.

The explanation also addresses a rounding convention: a level changes only after it is fully depleted or replenished, so fractional depth changes do not necessarily move the quote by a fractional tick. The source is a brief interpretation of one figure rather than a general derivation or empirical study, and it notes uncertainty about the notation used in that figure.

Key ideas

• Market orders consume displayed depth, while limit orders can replenish it.
• The net share imbalance is the sum of added and removed shares.
• Quote movement depends on complete depletion or replenishment of price levels.
• A fractional change in depth can correspond to a whole-tick quote change after rounding toward zero.
• The explanation interprets a specific figure and does not establish a general price-impact model.

Tags

# Order Flow Imbalance calculation


# Order Flow Imbalance calculation












I was wondering if anyone could help me understand Figure 2 Rama Cont's Price Impact paper? It is on arxiv as well.

In Figure 2 (screen from arxiv version), they demonstrate how to derive change in midprice and I do not understand why the result is $-\delta$? (-1 tick)?

$\delta \frac{L^{b}-M^{s}}{D}=\delta \frac{7-15}{5}=-\delta 1.6$ I understand the market order depletes one full tick, but they define $D$ as market depth and even tells us it is 5, but clearly they are using 8.

Could anyone point me in the right direction, please?

Thanks!

## Answer by Bob Jansen (score 4, accepted)

https://quant.stackexchange.com/a/75101

The way I understand this:

- $15$ shares are market sold in figure 1, this corresponds with $15 / 5 = 3$ ticks

- $7$ limit bid orders are added after step 1. This fully replenishes one level and partially replenishes a second one.

After this the best bid is $0 - 3 + 2 = 1$ tick lower than at the start.

I'm not sure why you say they are using 8, this seems to be the delta in shares offered, calculated as $-15 + 7 = 8$.

It seems they use $\lceil x \rceil$ to denote rounding of $x$ towards 0. Rounding towards zero is necessary as the bid or ask level only changes if a level is completely filled or emptied.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.