Forecasting Top-of-Book Changes from Bid–Ask Size

Summary

The document asks whether the size at the best bid and ask in a limit order book can be modeled to predict when the current top price level will disappear. It clarifies that quote entries have size, while volume refers to executed trades. One suggested empirical approach is to use historical order-book data to estimate the probability that the best price changes after a chosen time interval, conditioning on the relative displayed sizes at the top bid and ask.

The example illustrates how a size imbalance can be associated with different probabilities of a price-level change over a fixed horizon. This frames the task as conditional probability estimation rather than a deterministic prediction of whether the level will be consumed. The response offers a simple feature and modeling direction, but does not specify a complete stochastic-process model, data requirements, validation procedure, or evidence that the example probabilities generalize. Any practical forecast would need to be calibrated to the instrument, sampling horizon, and market conditions.

Key ideas

• Top-of-book quote levels contain displayed size, while volume refers to executed trades.
• Historical data can estimate the chance of a best-price change over a selected horizon.
• The bid-to-ask size ratio can serve as a conditioning feature for that estimate.
• A size imbalance changes the estimated probability but does not guarantee that a price level will be consumed.
• The example does not establish forecast performance across instruments or market conditions.

Tags

# modeling the volume of TOB of a LOB


# modeling the volume of TOB of a LOB












In Limit Order Books, orders at the same price are grouped and I call this group of orders a "price level"(I don't know if there's a name in literature). The total volume in this price level changes in time when aggressive trades occur or new orders are added to the price level. At some point in time, the TOB will be consumed completely and removed from the LOB or a better price enters the LOB and it becomes the new TOB. Is it possible to model the volume of TOB of a stock as a stochastic process? Actually, I wonder if it is possible to forecast if the TOB price will be consumed completely in a short period of time...

Thanks in advance

## Answer by chrisaycock (score 3)

https://quant.stackexchange.com/a/55524

Similar to the weighted mid, look at the size of the top bids and asks. ("Volume" refers to trades; quotes have "size".) Using historical data, you can determine the likelihood that the price level changes $X$ seconds later for a given size ratio.

For example, I may see that the level has a 10% chance of changing within 30 seconds when the aggregate size of the bids is 4 times that of the asks, and a 50% chance if the ratio is 40.

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.