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Optimal algorithmic trading and market microstructure

Author

Listed:
  • Mauricio Labadie

    () (CAMS - Centre d'analyse et de mathématique sociale - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

  • Charles-Albert Lehalle

    () (Head of Quantitative Research - CALYON group)

Abstract

The efficient frontier is a core concept in Modern Portfolio Theory. Based on this idea, we will construct optimal trading curves for different types of portfolios. These curves correspond to the algorithmic trading strategies that minimize the expected transaction costs, i.e. the joint effect of market impact and market risk. We will study five portfolio trading strategies. For the first three (single-asset, general multi-asseet and balanced portfolios) we will assume that the underlyings follow a Gaussian diffusion, whereas for the last two portfolios we will suppose that there exists a combination of assets such that the corresponding portfolio follows a mean-reverting dynamics. The optimal trading curves can be computed by solving an N-dimensional optimization problem, where N is the (pre-determined) number of trading times. We will solve the recursive algorithm using the "shooting method", a numerical technique for differential equations. This method has the advantage that its corresponding equation is always one-dimensional regardless of the number of trading times N. This novel approach could be appealing for high-frequency traders and electronic brokers.

Suggested Citation

  • Mauricio Labadie & Charles-Albert Lehalle, 2010. "Optimal algorithmic trading and market microstructure," Working Papers hal-00590283, HAL.
  • Handle: RePEc:hal:wpaper:hal-00590283 Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00590283v2
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    File URL: https://hal.archives-ouvertes.fr/hal-00590283v2/document
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    References listed on IDEAS

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    1. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
    2. Meier-Hellstern, K. S., 1987. "A fitting algorithm for Markov-modulated poisson processes having two arrival rates," European Journal of Operational Research, Elsevier, vol. 29(3), pages 370-377, June.
    3. Loisel, Stéphane & Milhaud, Xavier, 2011. "From deterministic to stochastic surrender risk models: Impact of correlation crises on economic capital," European Journal of Operational Research, Elsevier, vol. 214(2), pages 348-357, October.
    4. Cai, Jun & Tan, Ken Seng, 2007. "Optimal Retention for a Stop-loss Reinsurance Under the VaR and CTE Risk Measures," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 37(01), pages 93-112, May.
    5. Lindskog, Filip & McNeil, Alexander J., 2003. "Common Poisson Shock Models: Applications to Insurance and Credit Risk Modelling," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 33(02), pages 209-238, November.
    6. Xavier Milhaud & Stéphane Loisel & Véronique Maume-Deschamps, 2011. "Surrender triggers in life insurance: what main features affect the surrender behavior in a classical economic context?," Post-Print hal-00450003, HAL.
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    Cited by:

    1. Taiga Saito & Takanori Adachi & Teruo Nakatsuma & Akihiko Takahashi & Hiroshi Tsuda & Naoyuki Yoshino, 2017. "Trading and Ordering Patterns of Market Participants in High Frequency Trading Environment--Empirical Study in the Japanese Stock Market--," CIRJE F-Series CIRJE-F-1052, CIRJE, Faculty of Economics, University of Tokyo.
    2. Taiga Saito & Takanori Adachi & Teruo Nakatsuma & Akihiko Takahashi & Hiroshi Tsuda & Naoyuki Yoshino, 2017. "Trading and Ordering Patterns of Market Participants in High Frequency Trading Environment -Empirical Study in the Japanese Stock Market-," CARF F-Series CARF-F-411, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

    More about this item

    Keywords

    quantitative finance; optimal trading; algorithmic trading; systematic trading; market microstructure;

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