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Pré-Publication, Document De Travail Année : 2013

Pricing and hedging contingent claims with liquidity costs and market impact

Résumé

We 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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Dates et versions

hal-00802402 , version 1 (22-03-2013)
hal-00802402 , version 2 (02-04-2013)
hal-00802402 , version 3 (13-04-2013)
hal-00802402 , version 4 (09-09-2013)

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Frédéric Abergel, Grégoire Loeper. Pricing and hedging contingent claims with liquidity costs and market impact. 2013. ⟨hal-00802402v4⟩
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