Hedging through a Limit Order Book with Varying Liquidity

We relax the classical price-taking assumption and study the impact of orders of arbitrary size on price when the availability of liquidity is a concern in hedging. Our paper extends the earlier literature, suggesting that an environment with a permanent impact can be viewed as a special case with zero resilience, whereas an environment with a temporary impact can be viewed as a limit case with infinite resilience speed. Furthermore, our results hold for more general stochastic processes for the underlying asset: for example, for a generic Lévy process.