Liquidity Risk, Price Impacts and the Replication Problem

20 Pages Posted: 8 Sep 2011  

Alexandre F. Roch

University of Quebec at Montreal (UQAM) - Faculty of Management (ESG)

Date Written: September 7, 2011

Abstract

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.

Keywords: Liquidity risk, BSDEs, Stochastic volatility, Price impacts

JEL Classification: D40, G13

Suggested Citation

Roch, Alexandre F., Liquidity Risk, Price Impacts and the Replication Problem (September 7, 2011). Finance and Stochastics, Vol. 15, p. 399, 2011 . Available at SSRN: https://ssrn.com/abstract=1923836

Alexandre F. Roch (Contact Author)

University of Quebec at Montreal (UQAM) - Faculty of Management (ESG) ( email )

Case postale 8888
Succursale Centre-ville
Montreal, Quebec H3C 3P8
Canada

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