# 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

1. The average of the best bid and best offer
2. 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?

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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 ($\mbox{WP}$):

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

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
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Nice paper, thanks for the reference! –  Louis Marascio Oct 31 '13 at 17:57
This is interesting but debatable. The debate would be about which would you give more weightage to for representing the current price, the trades or the orders. Good food for thought. –  htrahdis Nov 2 '13 at 16:24