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@article{ Bouchaud2007, title = {Relation between Bid-Ask Spread, Impact and Volatility in Order-Driven Markets}, author = {Bouchaud, Jean-Philippe and Vettorazzo, Michele and Kockelkoren, Julien and Wyart, Matthieu and Potters, M}, journal = {Quantitative Finance}, number = {1}, pages = {41-57}, volume = {8}, year = {2007}, doi = {https://doi.org/10.1080/14697680701344515}, urn = {https://nbn-resolving.org/urn:nbn:de:0168-ssoar-221056}, 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 R2s exceeding 0.9. This correlation suggests both that the main determinant of the bid-ask spread is adverse selection, and that most of the volatility comes 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.}, }