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?