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Optimal Trade Execution under Stochastic Volatility and Liquidity

22 Pages Posted: 16 Mar 2013 Last revised: 2 Sep 2014

Patrick Cheridito

ETH Zurich; Swiss Finance Institute

Tardu Sepin

Bank of America Merrill Lynch

Date Written: January 21, 2014


We study the problem of optimally liquidating a financial position in a discrete-time model with stochastic volatility and liquidity. We consider the three cases where the objective is to minimize the expectation, an expected exponential and a mean-variance criterion of the implementation cost. In the first case, the optimal solution can be fully characterized by a forward-backward system of stochastic equations depending on conditional expectations of future liquidity. In the other two cases we derive Bellman equations from which the optimal solutions can be obtained numerically by discretizing the control space. In all three cases we compute optimal strategies for different simulated realizations of prices, volatility and liquidity and compare the outcomes to the ones produced by the deterministic strategies of Bertsimas and Lo and Almgren and Chriss.

Keywords: Optimal trade execution, implementation cost, discrete-time stochastic control, Bellman equation, stochastic volatility, stochastic liquidity

JEL Classification: G1

Suggested Citation

Cheridito, Patrick and Sepin, Tardu, Optimal Trade Execution under Stochastic Volatility and Liquidity (January 21, 2014). Applied Mathematical Finance, 2014, 21(4), 342--362. Available at SSRN: or

Patrick Cheridito

ETH Zurich ( email )

Department of Mathematics
8092 Zurich

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4

Tardu Sepin (Contact Author)

Bank of America Merrill Lynch ( email )

One Bryant Park
New York, NY 10036
United States

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