Depth-Weighted Prices from Limit Order Book Levels

Summary

The document compares common ways to define a price from an electronic limit order book. The best bid and offer midpoint is simple but ignores book depth, while the latest transaction price does not change when the book updates without a trade. The question asks for a measure that uses more of the book and can respond to order-book updates.

The accepted answer presents a weighted price calculated from prices and displayed quantities on both the demand and supply sides across selected book levels. Each level’s price contributes in proportion to its size, so the result reflects more depth than a top-of-book midpoint. The cited material gives the formula and defines its level, quantity, and price terms, but does not report empirical tests or establish that this measure predicts future prices. The choice of included levels and the quality of displayed liquidity therefore remain practical considerations.

Key ideas

• A bid-ask midpoint uses only the best quotes and omits deeper displayed liquidity.
• The latest trade price may stay unchanged when orders update without a transaction.
• A weighted book price averages bid and ask level prices using displayed quantities as weights.
• The document presents the measure as a candidate price function, without evidence of predictive performance.

Tags

# Price functions based on order book events


# Price functions based on order book events












Assume some equity traded on a given exchange based on an electronic limit open-order book $B$ that makes sequential updates as a function of time $t$. What are "natural" or common price functions $P: B \rightarrow \mathbb{R}_{\ge0}$?

Two natural price functions are

- The average of the best bid and best offer

- The price of the most recent transaction

A disadvantage of the first price function is that it doesn't take into account the whole depth of the book. A disadvantage of the second price function is that it only updates when a transaction occurs.

Are there more sophisticated price functions that take into account the whole depth of the book, and change for every update to the order book?

## Answer by Shane (score 11, accepted)

https://quant.stackexchange.com/a/9310

I recommend reading Cao, Hansch, and Wang (2004) "The Informational Content of an Open Limit Order Book". They present a simple model for an order-book price called the weighted price ($\mbox{WP}$):

$$ \mbox{WP}^{n_1 - n_2} = \frac{\sum_{j=n_1}^{n_2} (Q_j^d P_j^d + Q_j^s P_j^s)}{\sum_{j=n_1}^{n_2}(Q_j^d + Q_j^s)} $$

Where:

- $n$ is the order book level

- $Q_j$ is the size at level $j$

- $P_j$ is the price at level $j$

- $d$ is the "demand" side and $s$ is the "supply" side

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.