The Mathematical Institute, University of Oxford, Eprints Archive

A non-arbitrage liquidity model with observable parameters for derivatives

Bakstein, David and Howison, Sam (2003) A non-arbitrage liquidity model with observable parameters for derivatives. Mathematical Finance . (Submitted)



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 set-up empirically with high-frequency data of German blue chips and discuss further extensions to the model, including stochastic liquidity.

Item Type:Article
Uncontrolled Keywords:liquidity, option pricing, transaction costs
Subjects:O - Z > Partial differential equations
O - Z > Statistics
D - G > Game theory, mathematical finance, economics, social and behavioral sciences
Research Groups:Oxford Centre for Industrial and Applied Mathematics
Mathematical and Computational Finance Group
ID Code:53
Deposited By: Sam Howison
Deposited On:18 Mar 2004
Last Modified:29 May 2015 18:15

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