We extend the model of liquidity risk of Cetin et al. 5 to allow for price impacts. Starting from simple principles, we show that the impact of a trade on prices is directly proportional to the size of the transaction and the amount of liquidityof the asset. This leads to a new characterization of self-financing trading strategies and a sufficient condition for no arbitrage. We  show that, with the use of volatility swaps, contingent claims whose payoffs depend on the value of the asset can be approximately replicated  . The replicating costs of such payoffs are obtained from the solutions of BSDEs with 
We extend a linear version of the liquidity risk model of Cetin et al. (2004) to allow for price impacts. We show that the impact of a market order on prices depends on the size of the transaction and the level of liquidity. We obtain a simple characterization of self-financing trading strategies and a sufficient condition for no arbitrage. We consider a stochastic volatility model in which the volatility is partly correlated with the liquidity process and show that, with the use of variance swaps, contingent claims whose payoffs depend on the value of the asset can be approximately replicated in this setting . The replicating costs of such payoffs are obtained from the solutions of BSDEs with quadratic growth and analytical properties of these solutions are investigated.
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the model of liquidity risk
a linear version of the liquidity risk model
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5
(2004)
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Starting from simple principles, we
We
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trade on prices is directly proportional to
market order on prices depends on
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amount of liquidityof the asset. This leads to a new
level of liquidity. We obtain a simple
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consider a stochastic volatility model in which the volatility is partly correlated with the liquidity process and
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volatility
variance
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in this setting
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quadratic growth and analytical properties of these solutions are investigated.