A fractional reaction–diffusion description of supply and demand

Michael Benzaquen and Jean-Philippe Bouchaud ()
Additional contact information
Michael Benzaquen: Ladhyx, UMR CNRS 7646, École Polytechnique
Jean-Philippe Bouchaud: Capital Fund Management

The European Physical Journal B: Condensed Matter and Complex Systems, 2018, vol. 91, issue 2, 1-7

Abstract: Abstract We suggest that the broad distribution of time scales in financial markets could be a crucial ingredient to reproduce realistic price dynamics in stylised Agent-Based Models. We propose a fractional reaction–diffusion model for the dynamics of latent liquidity in financial markets, where agents are very heterogeneous in terms of their characteristic frequencies. Several features of our model are amenable to an exact analytical treatment. We find in particular that the impact is a concave function of the transacted volume (aka the “square-root impact law”), as in the normal diffusion limit. However, the impact kernel decays as t–β with β = 1∕2 in the diffusive case, which is inconsistent with market efficiency. In the sub-diffusive case the decay exponent β takes any value in [0, 1∕2], and can be tuned to match the empirical value β ≈ 1∕4. Numerical simulations confirm our theoretical results. Several extensions of the model are suggested.

Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://link.springer.com/10.1140/epjb/e2017-80246-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurphb:v:91:y:2018:i:2:d:10.1140_epjb_e2017-80246-9

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/10051

DOI: 10.1140/epjb/e2017-80246-9

Access Statistics for this article

The European Physical Journal B: Condensed Matter and Complex Systems is currently edited by P. Hänggi and Angel Rubio

More articles in The European Physical Journal B: Condensed Matter and Complex Systems from Springer, EDP Sciences
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().