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Seminar on Stochastic Analysis, Random Fields and Applications VII pp 411–434Cite as

Birkhäuser

Bid-Ask Spread Modelling, a Perturbation Approach

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Part of the book series: Progress in Probability ((PRPR,volume 67))

Abstract

Our objective is to study liquidity risk, in particular the so-called “bid-ask spread”, as a by-product of market uncertainties. “Bid-ask spread”, and more generally “limit order books” describe the existence of different sell and buy prices, which we explain by using different risk aversions of market participants. The risky asset follows a diffusion process governed by a Brownian motion which is uncertain. We use the error theory with Dirichlet forms to formalize the notion of uncertainty on the Brownian motion. This uncertainty generates noises on the trajectories of the underlying asset and we use these noises to expound the presence of bid-ask spreads. In addition, we prove that these noises also have direct impacts on the mid-price of the risky asset. We further enrich our studies with the resolution of an optimal liquidation problem under these liquidity uncertainties and market impacts. To complete our analysis, some numerical results will be provided.

Mathematics Subject Classification (2010). 60G15, 60H10, 60G45, 91G80.

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Author information

Authors and Affiliations

  1. Laboratoire d’Analyse et Probabilités, ENSIIE and Université d’Evry, 1 square de la Résistance, F-91025, Evry cedex, France

    Thomas Lim & Vathana Ly Vath

  2. Geneva School of Business Administration, Campus de Battelle Bâtiment F, 7 route de Drize, CH-1227, Carouge, Switzerland

    Jean-Michel Sahut

  3. Laboratoire Probabilités et Modèles Aléatoires, Université Paris Diderot – Paris 7, Case 7012, F-75205, Paris cedex 13, France

    Simone Scotti

Authors
  1. Thomas Lim
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  2. Vathana Ly Vath
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  3. Jean-Michel Sahut
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  4. Simone Scotti
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Corresponding author

Correspondence to Thomas Lim .

Editor information

Editors and Affiliations

  1. Institut de Mathématiques (IMA) Chaire de Statistiques Appliquées (STAP), Ecole Polytechnique Fédérale de Lausanne Fac. Sciences de Base (FSB), Lausanne, Switzerland

    Robert C. Dalang

  2. Institut Elie Cartan, Université de Lorraine, Vandoeuvre-les-Nancy CX, France

    Marco Dozzi

  3. Unité de Mathématiques appliquées, ENSTA ParisTech, Palaiseau, France

    Francesco Russo

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Lim, T., Vath, V.L., Sahut, JM., Scotti, S. (2013). Bid-Ask Spread Modelling, a Perturbation Approach. In: Dalang, R., Dozzi, M., Russo, F. (eds) Seminar on Stochastic Analysis, Random Fields and Applications VII. Progress in Probability, vol 67. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0545-2_21

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