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, in that illiquidity is modeled both in terms of depth and resilience. Some of our results hold for more general stochastic processes for the underlying, for example, a generic Lévy process and the model applies to a generic contingent claim. Furthermore, we offer an insight into the trade-off between hedging and price manipulation.