Exponential Resilience and Decay of Market Impact

  • Jim Gatheral
  • Alexander Schied
  • Alla Slynko
Part of the New Economic Windows book series (NEW)


Assuming a particular price process, it was shown by Gatheral in [6], that a model that combines nonlinear price impact with exponential decay of market impact admits price manipulation, an undesirable feature that should lead to rejection of the model. Subsequently, Alfonsi and Schied proved in [2] that their model of the order book which has nonlinear market impact and exponential resilience, is free of price manipulation. In this paper, we show how these at-first-sight incompatible results are in reality perfectly compatible.


Trading Strategy Price Process Price Impact Order Book Market Impact 
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  1. 1.
    Alfonsi A., Fruth A., Schied A. (2010) Optimal execution strategies in limit order books with general shape functions. Quantitative Finance 10:143–157CrossRefGoogle Scholar
  2. 2.
    Alfonsi A., Schied A. (2010) Optimal execution and absence of price manipulations in limit order book models. SIAM J. Financial Math. 1:490–522CrossRefGoogle Scholar
  3. 3.
    Alfonsi A., Schied A., Slynko A. (2009) Order book resilience, price manipulations, and the positive portfolio problem. Available at SSRN: papers.ssrn.com/sol3/papers.cfm?abstract id=1498514Google Scholar
  4. 4.
    Almgren R., Chee T., Hauptmann E., Li H. (2005) Equity market impact Risk Magazine July 2005:57–62Google Scholar
  5. 5.
    Bouchaud J.-P., Gefen Y., Potters M., Wyart M. (2004) Fluctuations and response in financial markets: the subtle nature of ‘random’ price changes. Quantitative Finance 4:176–190Google Scholar
  6. 6.
    Gatheral J. (2010) No-Dynamic-Arbitrage and Market Impact. Quantitative Finance 10: ForthcomingGoogle Scholar
  7. 7.
    Gatheral J., Schied A., Slynko A. (2010) Transient linear price impact and Fredholm integral equations. Available at SSRN: papers.ssrn.com/sol3/papers.cfm?abstract id=1531466Google Scholar
  8. 8.
    Obizhaeva A., Wang J. (2005) Optimal trading strategy and supply/demand dynamics. Available at SSRN: papers.ssrn.com/sol3/papers.cfm?abstract id=686168Google Scholar

Copyright information

© Springer-Verlag Italia 2011

Authors and Affiliations

  • Jim Gatheral
    • 1
  • Alexander Schied
    • 2
  • Alla Slynko
    • 2
  1. 1.Department of Mathematics, Baruch CollegeCUNYNew York
  2. 2.Department of MathematicsMannheim UniversityMannheimGermany

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