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Pricing and hedging contingent claims with liquidity costs and market impact

Frédéric Abergel () and Grégoire Loeper
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Frédéric Abergel: MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris, BNP Paribas
Grégoire Loeper: MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris

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Abstract: 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.

Keywords: Market impact; partial differential equations; liquidity costs (search for similar items in EconPapers)
Date: 2013-03-19
New Economics Papers: this item is included in nep-cwa and nep-mst
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DOI: 10.2139/ssrn.2239498

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