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Liquidity risk, price impacts and the replication problem

Abstract

We extend a linear version of the liquidity risk model of Çetin et al. (Finance Stoch. 8:311–341, 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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Correspondence to Alexandre F. Roch.

Additional information

This work was supported in part by the Fonds québécois de la recherche sur la nature et les technologies and NSF Grant DMS-0306194. Financial support from Crédit Suisse through the ETH Foundation is also gratefully acknowledged.

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Roch, A.F. Liquidity risk, price impacts and the replication problem. Finance Stoch 15, 399 (2011). https://doi.org/10.1007/s00780-011-0156-x

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  • DOI: https://doi.org/10.1007/s00780-011-0156-x

Keywords

  • Liquidity risk
  • BSDEs
  • Stochastic volatility
  • Price impacts

Mathematics Subject Classification (2000)

  • 60H30
  • 60G35
  • 91B24
  • 91B30

JEL Classification

  • D40
  • G13