Optimal split of orders across liquidity pools: a stochastic algorithm approach
Evolutions of the trading landscape lead to the capability to exchange the same financial instrument on different venues. Because of liquidity issues, the trading firms split large orders across several trading destinations to optimize their execution. To solve this problem we devised two stochastic recursive learning procedures which adjust the proportions of the order to be sent to the different venues, one based on an optimization principle, the other on some reinforcement ideas. Both procedures are investigated from a theoretical point of view: we prove a.s. convergence of the optimization algorithm under some light ergodic (or "averaging") assumption on the input data process. No Markov property is needed. When the inputs are i.i.d. we show that the convergence rate is ruled by a Central Limit Theorem. Finally, the mutual performances of both algorithms are compared on simulated and real data with respect to an "oracle" strategy devised by an "insider" who knows a priori the executed quantities by every venues.
|Date of creation:||18 Mar 2010|
|Note:||View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00422427v3|
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- Thierry Foucault & Albert J. Menkveld, 2008.
"Competition for Order Flow and Smart Order Routing Systems,"
Journal of Finance,
American Finance Association, vol. 63(1), pages 119-158, 02.
- Foucault, Thierry & Menkveld, Albert J., 2006. "Competition for Order Flow and Smart Order Routing Systems," CEPR Discussion Papers 5523, C.E.P.R. Discussion Papers.
- Thierry Foucault & Albert J. Menkveld, 2008. "Competition for Order Flow and Smart Order Routing Systems," Post-Print hal-00459801, HAL.
- Foucault, Thierry & Menkveld, Albert, 2006. "Competition for order flow and smart order routing systems," Les Cahiers de Recherche 831, HEC Paris.
- Thierry Foucault, 2010. "Competition for Order Flow and Smart Order Routing Systems," Post-Print hal-00554030, HAL.