Styled Algorithmic Trading and the MV-MVP Style

18 Pages Posted: 9 Oct 2014

See all articles by Jackie Shen

Jackie Shen

Financial Services, New York

Yingjie Yu

University of Illinois at Urbana-Champaign

Date Written: October 7, 2014


Except for pre-trade assessment, algorithmic trading for optimal execution has to be dynamically adapted to real-time market environments and inventory positions. This makes dynamic programming (DP) the most natural approach. Due to the curse of dimensionality, however, it is highly challenging to design a rigorous DP strategy that invites a tractable solution procedure. Approximate dynamic programming (ADP) has hence emerged as a practical solution, and the proposed framework of styled trading follows the ADP paradigm.

A styled model makes a particular choice for its state variables as well as the parametric forms of its trading policies. Its calibration then becomes a nonlinear, constrained, but lower-dimensional optimization problem. The current framework also goes beyond the additive objectives normally required by a traditional DP strategy and its associated Bellman solution procedure. It works with the mean-variance utilities of Almgren and Chriss (J. Risk, 3, 2000) to effectively express risk aversion of a typical trader. The new framework is demonstrated through building one particular style called MV-MVP, i.e., the mean-variance (MV) objective formulated upon the state variables of moneyness and volume participation (MVP). The MV-MVP style generalizes the VWAP strategy by facilitating dynamic reactions to moneyness and by embodying the popular street practice of trading aggressively or passively while in the money. Numerical calibration based on stochastic gradient descent and binomial-tree gradient descent is discussed. Simulated dynamic trading paths help illustrate the general behavior of the MV-MVP style.

Keywords: Dynamic programming, style, moneyness, aggressive, passive, participation, parametric, stochastic, gradient descent, binomial trees

JEL Classification: G24, C61

Suggested Citation

Shen, Jackie and Yu, Yingjie, Styled Algorithmic Trading and the MV-MVP Style (October 7, 2014). Available at SSRN: or

Jackie Shen (Contact Author)

Financial Services, New York ( email )

United States


Yingjie Yu

University of Illinois at Urbana-Champaign ( email )

601 E John St
Champaign, IL Champaign 61820
United States

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