Pricing and Hedging Contingent Claims with Liquidity Costs and Market Impact
13 Pages Posted: 26 Mar 2013 Last revised: 15 Apr 2013
Date Written: April 13, 2013
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
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