From Walras' auctioneer to continuous time double auctions: A general dynamic theory of supply and demand

TL;DR

This paper develops a dynamic supply and demand model with heterogeneous agents, revealing that in continuous trading, supply and demand vanish quadratically near the price, explaining the universal square-root price impact observed in markets like Bitcoin.

Contribution

It introduces a dynamic theory incorporating transactions and heterogeneous beliefs, extending Walrasian auctions to continuous time, and empirically confirms quadratic supply and demand near the price.

Findings

Supply and demand vanish quadratically near the price in continuous trading.

Price impact behaves as the square root of excess volume.

Market clearing makes prices hypersensitive to small fluctuations.

Abstract

In standard Walrasian auctions, the price of a good is defined as the point where the supply and demand curves intersect. Since both curves are generically regular, the response to small perturbations is linearly small. However, a crucial ingredient is absent of the theory, namely transactions themselves. What happens after they occur? To answer the question, we develop a dynamic theory for supply and demand based on agents with heterogeneous beliefs. When the inter-auction time is infinitely long, the Walrasian mechanism is recovered. When transactions are allowed to happen in continuous time, a peculiar property emerges: close to the price, supply and demand vanish quadratically, which we empirically confirm on the Bitcoin. This explains why price impact in financial markets is universally observed to behave as the square root of the excess volume. The consequences are important, as they imply that the very fact of clearing the market makes prices hypersensitive to small fluctuations.