# What is the order flow imbalance?

The price impact of order book event is an arxiv article which shows that, over short time intervals, price changes are mainly driven by the order flow imbalance, defined as the imbalance between the supply and demand at the best bid and ask prices.

I did not fully understand what was the order flow imbalance. It seems a wonderful tool to tell when the price movement will change significantly. Is anyone able to explain mathematically and intuitively how it works?

• Order flow imbalance is both defined mathematically and explained in the 2nd last paragraph of page 4 of the paper you referenced. Jan 28 '19 at 21:09

Intuitively, if there is 10x more depth at the bid than the ask, and trades arrive at (and are sized at) random, it is 10x more likely that the price will tick up than down.

In practice, often trades do not arrive at random and in fact show strong directional auto-correlation. Moreover, the depth at the bid/ask are not static quantities, they are constantly changing.

• If you can integrate the formula and tell me how to use it in practice, it might be nice. :D Jan 29 '19 at 13:50

They are mainly two kinds of imbalances that are important in the price formation

• the imbalance of liquidity providers (filling the orderbook in a LOB-driven market)
• the imbalance of liquidity consumers (sending marketable orders in a LOB-driven market).

It is quite obvious that these two imbalances are shaping the prices: if you do not change liquidity offering, the more buying consumers and the higher to price will go up (same for sellers and the price going down). And if you do not change the conuming flow, the liquidity provision imbalance will lead one queue to depletes before the other, driving the price up or down.

Moreover, you have to keep in mind that, since the best strategy to buy or sell a large quantity of shares or contracts is to split them (according to a balance between trading costs and opportunity costs), and because trading algorithms (and traders) mix limit and marketable orders in LOBs, the same "agent" usually contributes to both: a buying agent will provide liquidity at the bid and consume some at the ask during the same day: these effects are deeply mixed.

The point is how to to capture these imbalances with not too noisy estimators.

• the imbalance of liquidity can easily be captured by the imbalance between the bid side and the ask side (orderbook imbalance), on "large tick instruments", it is enough to focus on the first limits. See the second section of "Incorporating signals into optimal trading" by Neuman and L in Finance and Stochastics 23.2 (2019): 275-311 for illustrations.
• the imbalance of liquidity consumption can be captured by a difference between the sides of recent trades, and it is what propagator models are capturing.

The intrication of both imbalances are captured by the Queue Reactive (QR) model, linking the flows (or liquidity providing orders, but also of liquidity consuming orders) with the state of the orderbook.

The Order Flow Imbalance being the infinitesimal increment of liquidity provision, it is linked with the orderbook imbalance (ie if you sum the OFI between $$t_0$$ and $$t_1$$ you obtain the difference between the quantities on the two orberbooks: $$OB_1-OB_0$$). It is clearly capturing a part of the formation process. Moreover, because of the relation $$OFI(t_0\rightarrow t_1)=OB_1-OB_0$$, it can be used to describe the trajectory of the orderbook in a bid-ask quadrant: put the quantity at the bid on the x-axis and the quantity at the ask on the y-axis:

• the state of the orderbook is a point $$X=(Q^A,Q^B)$$ of this quadrant
• the moves of this point are exactly specified by the OFI, i.e.: $$dX=OFI\,dt$$.

This view has some limitation: it has been shown by the QR Model that the first limit is not enough, and that the "jumps" consecutive to the full depletion of one of the two queues (first bid or first ask), is conditioned by the shape of the orderbook.

In the second edition of Market Microstructure in Practice (L and Laruelle, 2018) the chapter "The Price Formation Process and Orderbooks Dynamics" describes all this in detail.

On the paper, OFI is defined as

a single variable, the order flow imbalance (OFI), which represents the net order flow at the bid and ask and tracks changes in the size of the bid and ask queues by

• increasing every time the bid size increases, the ask size decreases or the bid/ask prices increase

• decreases every time the bid size decreases, the ask size increases or the bid/ask prices decrease.

From the explanation, the OFI is decided by three variables: 1. offer size, 2. bid size 3. bid/ask price.

The quantity is more like OBV rather than money flow. Money flow is quantity multiplying price and volume while obv adds volumes with the volume sign decided by price difference.

The OFI calculates OBV like quantities for the offer side and bid side separately and adds them together in a nutshell.

They claim that linear relationship between a price change and OFI and it seems quite plausible. But the article only presents the in-sample results. It doesn't talk of any forecasting performance while the forecast is our main concern in trading.

In any case, it's good to know there is a linear relationship between OFI and price change in terms of curiosity.