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A Risk-Neutral Parametric Liquidity Model for Derivatives

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Author Info
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.

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Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2002mf02.

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Date of creation: 2002
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Handle: RePEc:sbs:wpsefe:2002mf02

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  5. Lo, Andrew W & Wang, Jiang, 1995. " Implementing Option Pricing Models When Asset Returns Are Predictable," Journal of Finance, American Finance Association, vol. 50(1), pages 87-129, March. [Downloadable!] (restricted)
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  6. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March. [Downloadable!] (restricted)
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  17. Werner Stanzl & Gur Huberman, 2000. "Arbitrage-Free Price-Update and Price-Impact Functions," Yale School of Management Working Papers ysm164, Yale School of Management. [Downloadable!]
  18. J. Doyne Farmer & Shareen Joshi, 2000. "The Price Dynamics of Common Trading Strategies," Working Papers 00-12-069, Santa Fe Institute.
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  19. Leland, Hayne E, 1985. " Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December. [Downloadable!] (restricted)
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  20. Frey, Rüdiger, 1996. "The Pricing and Hedging of Options in Finitely Elastic Markets," Discussion Paper Serie B 372, University of Bonn, Germany. [Downloadable!]
  21. K. Ronnie Sircar, George Papanicolaou, 1998. "General Black-Scholes models accounting for increased market volatility from hedging strategies," Applied Mathematical Finance, Taylor and Francis Journals, vol. 5(1), pages 45-82, March. [Downloadable!] (restricted)
  22. Jarrow, Robert A., 1994. "Derivative Security Markets, Market Manipulation, and Option Pricing Theory," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(02), pages 241-261, June. [Downloadable!]
  23. Marcus G. Daniels & J. Doyne Farmer & Giulia Iori & Eric Smith, 2002. "Demand Storage, Market Liquidity, and Price Volatility," Working Papers 02-01-001, Santa Fe Institute.
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