Estimating the efficient price from the order flow: a Brownian Cox process approach

TL;DR

This paper introduces a new concept of an efficient price at ultra high frequency, estimated from order flow data using a Brownian Cox process model, addressing ambiguity in defining asset prices.

Contribution

It proposes a novel notion of efficient price and develops a statistical methodology to estimate it from order flow data using a Brownian Cox process framework.

Findings

Defines a practical efficient price concept

Develops a statistical estimation methodology

Demonstrates effectiveness on high-frequency data

Abstract

At the ultra high frequency level, the notion of price of an asset is very ambiguous. Indeed, many different prices can be defined (last traded price, best bid price, mid price,...). Thus, in practice, market participants face the problem of choosing a price when implementing their strategies. In this work, we propose a notion of efficient price which seems relevant in practice. Furthermore, we provide a statistical methodology enabling to estimate this price form the order flow.