OPTIMAL EXECUTION OF A VWAP ORDER: A STOCHASTIC CONTROL APPROACH |
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Authors: | Christoph Frei Nicholas Westray |
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Affiliation: | 1. Department 2. of Mathematical and Statistical 3. SciencesUniversity of Alberta;4. Deutsche Bank AG, London |
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Abstract: | We consider the optimal liquidation of a position of stock (long or short) where trading has a temporary market impact on the price. The aim is to minimize both the mean and variance of the order slippage with respect to a benchmark given by the market volume‐weighted average price (VWAP). In this setting, we introduce a new model for the relative volume curve which allows simultaneously for accurate data fit, economic justification, and mathematical tractability. Tackling the resulting optimization problem using a stochastic control approach, we derive and solve the corresponding Hamilton–Jacobi–Bellman equation to give an explicit characterization of the optimal trading rate and liquidation trajectory. |
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Keywords: | optimal trade execution VWAP HJB equation gamma bridge |
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