Pricing and hedging contingent claims with liquidity costs and market impact
AbstractWe study the influence of taking liquidity costs and market impact into account when hedging a contingent claim, first in the discrete time setting, then in continuous time. In the latter case and in a complete market, we derive a fully non-linear pricing partial differential equation, and characterizes its parabolic nature according to the value of a numerical parameter naturally interpreted as a relaxation coefficient for market impact. We then investigate the more challenging case of stochastic volatility models, and prove the parabolicity of the pricing equation in a particular case.
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Date of creation: 19 Mar 2013
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Market impact; partial differential equations; liquidity costs;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-04-06 (All new papers)
- NEP-CWA-2013-04-06 (Central & Western Asia)
- NEP-MST-2013-04-06 (Market Microstructure)
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