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A Risk-Neutral Parametric Liquidity Model for Derivatives


  • David Bakstein
  • Sam Howison


We develop a parameterised model for liquidity effects arising from the trading in an asset. Liquidity is defined via a combination of a trader's individual transaction cost and a price slippage impact, which is felt by all market participants. The chosen definition allows liquidity to be observable in a centralised order-book of an asset as is usually provided in most non-specialist exchanges. The discrete-time version of the model is based on the CRR binomial tree and in the appropriate continuous-time limits we derive various nonlinear partial differential equations. Both versions can be directly applied to the pricing and hedging of options; the nonlinear nature of liquidity leads to natural bid-ask spreads that are based on the liquidity of the market for the underlying and the existence of (super-)replication strategies. We test and calibrate our model empirically with high-frequency data of German blue chips and discuss further extensions to the model, including stochastic liquidity.

Suggested Citation

  • David Bakstein & Sam Howison, 2002. "A Risk-Neutral Parametric Liquidity Model for Derivatives," OFRC Working Papers Series 2002mf02, Oxford Financial Research Centre.
  • Handle: RePEc:sbs:wpsefe:2002mf02

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    References listed on IDEAS

    1. Harrison Hong & Jeremy C. Stein, 2003. "Differences of Opinion, Short-Sales Constraints, and Market Crashes," Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 487-525.
    2. Gennotte, Gerard & Leland, Hayne, 1990. "Market Liquidity, Hedging, and Crashes," American Economic Review, American Economic Association, vol. 80(5), pages 999-1021, December.
    3. Glosten, Lawrence R. & Milgrom, Paul R., 1985. "Bid, ask and transaction prices in a specialist market with heterogeneously informed traders," Journal of Financial Economics, Elsevier, vol. 14(1), pages 71-100, March.
    4. Boldrin, Michele & Levine, David K., 2001. "Growth Cycles and Market Crashes," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 13-39, January.
    5. David H. Cutler & James M. Poterba & Lawrence H. Summers, 1988. "What Moves Stock Prices?," Working papers 487, Massachusetts Institute of Technology (MIT), Department of Economics.
    6. Demange Gabrielle & Laroque Guy, 1995. "Private Information and the Design of Securities," Journal of Economic Theory, Elsevier, vol. 65(1), pages 233-257, February.
    7. Martin Chalkley & In Ho Lee, 1998. "Learning and Asymmetric Business Cycles," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 1(3), pages 623-645, July.
    8. Veldkamp, Laura L., 2005. "Slow boom, sudden crash," Journal of Economic Theory, Elsevier, vol. 124(2), pages 230-257, October.
    9. Joseph Zeira, 2000. "Informational overshooting, booms and crashes," Proceedings, Federal Reserve Bank of San Francisco, issue Apr.
    10. Admati, Anat R, 1985. "A Noisy Rational Expectations Equilibrium for Multi-asset Securities Markets," Econometrica, Econometric Society, vol. 53(3), pages 629-657, May.
    11. Van Nieuwerburgh, Stijn & Veldkamp, Laura, 2006. "Learning asymmetries in real business cycles," Journal of Monetary Economics, Elsevier, vol. 53(4), pages 753-772, May.
    12. Veronesi, Pietro, 1999. "Stock Market Overreaction to Bad News in Good Times: A Rational Expectations Equilibrium Model," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 975-1007.
    13. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. William T. Shaw, 2008. "A model of returns for the post-credit-crunch reality: Hybrid Brownian motion with price feedback," Papers 0811.0182,, revised Aug 2009.
    2. William T. Shaw & Marcus Schofield, 2015. "A model of returns for the post-credit-crunch reality: hybrid Brownian motion with price feedback," Quantitative Finance, Taylor & Francis Journals, vol. 15(6), pages 975-998, June.

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