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Relation between Bid-Ask Spread, Impact and Volatility in Double Auction Markets

Matthieu Wyart·Jean-Philippe Bouchaud·Julien Kockelkoren·Marc Potters·Michele Vettorazzo
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Abstract

We show that the cost of market orders and the profit of infinitesimal market-making or -taking strategies can be expressed in terms of directly observable quantities, namely the spread and the lag-dependent impact function. Imposing that any market taking or liquidity providing strategies is at best marginally profitable, we obtain a linear relation between the bid-ask spread and the instantaneous impact of market orders, in good agreement with our empirical observations on electronic markets. We then use this relation to justify a strong, and hitherto unnoticed, empirical correlation between the spread and the volatility_per trade_, with R^2s exceeding 0.9. This correlation suggests both that the main determinant of the bid-ask spread is adverse selection, and that most of the volatilitycomes from trade impact. We argue that the role of the time-horizon appearing in the definition of costs is crucial and that long-range correlations in the order flow, overlooked in previous studies, must be carefully factored in. We find that the spread is significantly larger on the nyse, a liquid market with specialists, where monopoly rents appear to be present.

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Matthieu Wyart, Jean-Philippe Bouchaud, Julien Kockelkoren, Marc Potters, Michele Vettorazzo. 2007-03-12. Relation between Bid-Ask Spread, Impact and Volatility in Double Auction Markets. https://arxiv.org/abs/physics/0603084

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