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A Risk-Neutral Parametric Liquidity Model for Derivatives

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  • David Bakstein
  • Sam Howison

Abstract

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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    File URL: http://www.finance.ox.ac.uk/file_links/finecon_papers/2002mf02.pdf
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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, arXiv.org, 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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