Pricing and Hedging Contingent Claims with Liquidity Costs and Market Impact

13 Pages Posted: 26 Mar 2013 Last revised: 15 Apr 2013

See all articles by Frederic Abergel

Frederic Abergel

BNP Paribas AM

Gregoire Loeper

Monash University - School of Mathematical Sciences; BNP Paribas

Date Written: April 13, 2013

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: derivatives, market impact, liquidity

JEL Classification: G13

Suggested Citation

Abergel, Frederic and Loeper, Gregoire, Pricing and Hedging Contingent Claims with Liquidity Costs and Market Impact (April 13, 2013). Available at SSRN: https://ssrn.com/abstract=2239498 or http://dx.doi.org/10.2139/ssrn.2239498

Frederic Abergel (Contact Author)

BNP Paribas AM ( email )

Paris
France

Gregoire Loeper

Monash University - School of Mathematical Sciences ( email )

Clayton Campus
Victoria, 3800
Australia

BNP Paribas ( email )

Paris
France

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