IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Optimal trading algorithms and selfsimilar processes: a p-variation approach

Listed author(s):
  • Mauricio Labadie


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

  • Charles-Albert Lehalle


    (Head of Quantitative Research - CALYON group)

Almgren and Chriss ("Optimal execution of portfolio transactions", Journal of Risk, Vol. 3, No. 2, 2010, pp. 5-39) and Lehalle ("Rigorous strategic trading: balanced portfolio and mean reversion", Journal of Trading, Summer 2009, pp. 40-46.) developed optimal trading algorithms for assets and portfolios driven by a brownian motion. More recently, Gatheral and Schied ("Optimal trade execution under geometric brownian motion in the Almgren and Chriss framework", Working paper SSRN, August 2010) addressed the same problem for the geometric brownian motion. In this article we extend these ideas for assets and portfolios driven by a discrete version of a selfsimilar process of exponent H in (0,1), which can be either a fractional brownian motion of Hurst exponent H or a truncated Lévy distribution of index 1/H. The cost functional we use is not the classical expectation-variance one: instead of the variance, we use the p-variation, i.e. the Lp equivalent of the variance. We find explicitly the trading algorithm for any p>1 and compare the resulting trading curve (that we call p-curve) with the classical expectation-variance curve (the 2-curve). If p2 then the p-curve is above the 2-curve at the beginning of the execution and below at the end. Therefore, this pattern minimizes the market impact. We also show that the value of p in the p-variation is related to the exponent H of selfsimilarity via p=1/H. In consequence, one can find the right value of p to put into the trading algorithm by calibrating the exponent H via real time series. We believe this result is interesting applications for high-frecuency trading.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Paper provided by HAL in its series Working Papers with number hal-00546145.

in new window

Date of creation: 10 Dec 2010
Handle: RePEc:hal:wpaper:hal-00546145
Note: View the original document on HAL open archive server:
Contact details of provider: Web page:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

in new window

  1. Jim Gatheral & Alexander Schied, 2011. "Optimal Trade Execution Under Geometric Brownian Motion In The Almgren And Chriss Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 353-368.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-00546145. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.