[Paper Review] Relation between Bid-Ask Spread, Impact and Volatility in Double Auction Markets

Matthieu Wyart, Jean‐Philippe Bouchaud+3 more|arXiv (Cornell University)|Mar 10, 2006

Financial Markets and Investment Strategies28 references17 citations

TL;DR

The paper proposes a linear relationship between bid-ask spreads and market order impact in electronic double auctions, driven by symmetry in effective costs between limit and market orders. Empirical evidence supports a proportionality between spread and volatility per trade, indicating adverse selection as the primary driver of spreads when volatility per trade measures information content in prices.

ABSTRACT

We argue that on electronic markets, limit and market orders should have equal effective costs on average. This symmetry implies a linear relation between the bid-ask spread and the average impact of market orders. Our empirical observations on different markets are consistent with this hypothesis. We then use this relation to justify a simple, and hitherto unnoticed, proportionality relation between the spread and the volatility_per trade_. We provide convincing empirical evidence for this relation. This suggests that the main determinant of the bid-ask spread is adverse selection, if one considers that the volatility per trade is a measure of the amount of `information' included in prices at each transaction. Symmetry between market and limit orders stems from the self-organization of liquidity in electronic markets. Our results appear to hold approximately on liquid specialist markets as well, although the spread is significantly larger.

Motivation & Objective

• To investigate the symmetry in effective costs between limit and market orders in electronic markets.
• To establish a theoretical link between bid-ask spreads and the average impact of market orders.
• To test whether spread is proportional to volatility per trade as a proxy for information content in prices.
• To assess the robustness of this relationship across liquid electronic and specialist markets.

Proposed method

• Theoretical modeling based on symmetry in order costs between limit and market orders in electronic markets.
• Empirical estimation of the linear relationship between bid-ask spread and market order impact across multiple electronic markets.
• Use of volatility per trade as a proxy for information flow in price discovery.
• Empirical testing of the proportionality between spread and volatility per trade using market data.
• Comparison of results across electronic markets and liquid specialist markets to assess generalizability.

Experimental results

Research questions

• RQ1 Is there a linear relationship between bid-ask spread and average market order impact in electronic double auctions?
• RQ2 Does the spread scale proportionally with volatility per trade, suggesting adverse selection as the main determinant?
• RQ3 To what extent does the symmetry between limit and market order costs hold in real market data?
• RQ4 How does the spread-volatility relationship differ between electronic and specialist markets?

Key findings

• A linear relationship between bid-ask spread and average market order impact is empirically supported across multiple electronic markets.
• The spread is found to be proportional to volatility per trade, indicating that information content in prices drives the spread.
• The main determinant of the bid-ask spread is adverse selection, when volatility per trade measures information in price changes.
• The symmetry between limit and market order costs arises from the self-organization of liquidity in electronic markets.
• The same proportionality holds approximately in liquid specialist markets, though spreads are significantly larger.