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

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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 orderbook of an asset as is usually provided in most nonspecialist exchanges. The discretetime version of the model is based on the CRR binomial tree and in the appropriate continuoustime 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 bidask 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 setup empirically with highfrequency 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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