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OPTIMAL EXECUTION OF A VWAP ORDER: A STOCHASTIC CONTROL APPROACH
Author(s) -
Frei Christoph,
Westray Nicholas
Publication year - 2015
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12048
Subject(s) - volume weighted average price , stochastic control , econometrics , position (finance) , trading strategy , order (exchange) , mathematical optimization , algorithmic trading , economics , optimal control , computer science , mathematics , stock market , financial economics , market maker , finance , paleontology , biology , horse
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.