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Liquidity risk theory and coherent measures of risk


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  • Carlo Acerbi
  • Giacomo Scandolo


We discuss liquidity risk from a pure risk-theoretical point of view in the axiomatic context of coherent measures of risk. We propose a formalism for liquidity risk that is compatible with the axioms of coherency. We emphasize the difference between 'coherent risk measures' (CRM) ρ(X ) defined on portfolio values X as opposed to 'coherent portfolio risk measures' (CPRM) ρ(p) defined on the vector space of portfolios p, and we observe that in the presence of liquidity risk the value function on the space of portfolios is no longer necessarily linear. We propose a new nonlinear 'Value' function VL(p) that depends on a new notion of 'liquidity policy' L. The function VL(p) naturally arises from a general description of the impact that the microstructure of illiquid markets has when marking a portfolio to market. We discuss the consequences of the introduction of the function VL(p) in the coherency axioms and we study the properties induced on CPRMs. We show in particular that CPRMs are convex, finding a result that was proposed as a new axiom in the literature of so called 'convex measures of risk'. The framework we propose is not a model but rather a new formalism, in the sense that it is completely free from hypotheses on the dynamics of the market. We provide interpretation and characterization of the formalism as well as some stylized examples.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

Volume (Year): 8 (2008)
Issue (Month): 7 ()
Pages: 681-692

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Handle: RePEc:taf:quantf:v:8:y:2008:i:7:p:681-692

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Keywords: Liquidity risk; Portfolio value; Coherent risk measures;


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Cited by:
  1. Péter Csóka & P. Jean-Jacques Herings, 2014. "Risk Allocation under Liquidity Constraints," Working Papers 2014.47, Fondazione Eni Enrico Mattei.
  2. Csóka, Péter & Pintér, Miklós, 2010. "On the impossibility of fair risk allocation," MPRA Paper 26515, University Library of Munich, Germany.
  3. Stange, Sebastian & Kaserer, Christoph, 2008. "Why and how to integrate liquidity risk into a VaR-framework," CEFS Working Paper Series 2008-10, Center for Entrepreneurial and Financial Studies (CEFS), Technische Universität München.
  4. Damiano Brigo & Mirela Predescu & Agostino Capponi, 2010. "Credit Default Swaps Liquidity modeling: A survey," Papers 1003.0889,, revised Mar 2010.
  5. Fabio Caccioli & Jean-Philippe Bouchaud & J. Doyne Farmer, 2012. "A proposal for impact-adjusted valuation: Critical leverage and execution risk," Papers 1204.0922,, revised Aug 2012.
  6. Bianchetti, Marco & Carlicchi, Mattia, 2012. "Markets Evolution After the Credit Crunch," MPRA Paper 44023, University Library of Munich, Germany.
  7. Marco Bianchetti & Mattia Carlicchi, 2013. "Markets Evolution After the Credit Crunch," Papers 1301.7078,
  8. Marco, Bianchetti & Mattia, Carlicchi, 2012. "Interest Rates After The Credit Crunch: Multiple-Curve Vanilla Derivatives and SABR," MPRA Paper 42248, University Library of Munich, Germany.
  9. Kountzakis, C. & Polyrakis, I.A., 2013. "Coherent risk measures in general economic models and price bubbles," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 201-209.
  10. Csóka, Péter & Bátyi, Tamás László & Pintér, Miklós & Balog, Dóra, 2011. "Tőkeallokációs módszerek és tulajdonságaik a gyakorlatban
    [Methods of capital allocation and their characteristics in practice]
    ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 619-632.
  11. Csóka, Péter & Havran, Dániel & Váradi, Kata, 2013. "Konferencia a pénzügyi piacok likviditásáról. Third Annual Financial Market Liquidity Conference BCE Befektetések és Vállalati Pénzügy Tanszék-MTA KRTK KTI Játékelméleti Kutatócsoport-N," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(4), pages 477-485.


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