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Optimal Trade Execution under Stochastic Volatility and Liquidity

Author(s): Cheridito, Patrick; Sepin, Tardu

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Abstract: 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 or 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 (1998; Optimal control of execution costs. Journal of Financial Markets, 1, 1–50) and Almgren and Chriss (2001; Optimal execution of portfolio transactions. Journal of Risk, 3, 5–33).
Publication Date: 2014
Citation: Cheridito, Patrick, and Tardu Sepin. "Optimal trade execution under stochastic volatility and liquidity." Applied Mathematical Finance 21, no. 4 (2014): 342-362. doi:10.1080/1350486X.2014.881005
DOI: doi:10.1080/1350486X.2014.881005
ISSN: 1350-486X
EISSN: 1466-4313
Pages: 342 - 362
Type of Material: Journal Article
Journal/Proceeding Title: Applied Mathematical Finance
Version: Author's manuscript

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