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

By Matthieu Wyart, Jean-Philippe Bouchaud, J. Kockelkoren, Marc Potters, Michele Vettorazzo. 2006

143 citations recorded by the source corpus.

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 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.

Subfields: Accounting, Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/472402c34dda6d4bcdfd04e994823e01aeac35ee

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Citations in the corpus

A Dynamic Model of the Limit Order Book (2009, unknown): “Empirical evidence for both results can be found in Wyart et al. (2008, equations 32 and 33), for high-frequency data. Interestingly, the first result is in contradiction with a large literature that documents a positive relation between trading volume and volatility when dealing with lower-frequenc”
Limit order books (2010, background): “…2001, Sandås 2001, Evans and Lyons 2002, Foucault et al. 2005, Goettler et al. 2006, Hall and Hautsch 2006, Hollifield et al. 2006, Cao et al. 2008, Wyart et al. 2008, Alfonsi et al. 2010, Gatheral 2010, Roşu 2010); an understanding of the state of L(t) and order flow provides insight into the…”
Limit theorems for nearly unstable Hawkes processes (2013, background): “Also, it is widely acknowledged that there exists a linear relationship between the cumulated order flow and the integrated squared volatility, see for example [41].”
Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes (2015, background): “[40]), and CIR processes are very classical models for the squared volatility.”