Relation between bid-ask spread, impact and volatility in order-driven markets

Matthieu Wyart, Jean Philippe Bouchaud, Julien Kockelkoren, Marc Potters, Michele Vettorazzo

    Research output: Contribution to journalArticlepeer-review


    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.

    Original languageEnglish (US)
    Pages (from-to)41-57
    Number of pages17
    JournalQuantitative Finance
    Issue number1
    StatePublished - Feb 2008


    • Bid-ask spread
    • Impact
    • Liquidity
    • Microstructure

    ASJC Scopus subject areas

    • General Economics, Econometrics and Finance
    • Finance


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