Optimization of Conditional Trajectories in a Market Place of Multiple Liquidity Pools

Abstract

<p>Algorithmic Trading is the automated process of trading exogenous<br />orders in electronic (stock) exchanges.The primary objective in execution<br />of orders is to achieve the most ecient price. We propose two optimal<br />strategies for the execution of atomic orders based on minimization of impact<br />and volatility costs, in both single and multiple market environments.<br />The rst considered strategy is based on a relatively simple nonlinear optimization<br />model while the second allows re-optimization at some time point<br />within a given execution time. Finally, we consider how the model that allows<br />re-optimization perform in a multiple trading venue environment. In all<br />cases, a combination of market and limit orders are used. The key innovation<br />in our approach is the introduction of a Fill Probability function which<br />allows a combination of market and limit orders in the four optimization<br />models we are discussing in this thesis. Under certain conditions the objective<br />functions of all considered problems are convex and therefore standard<br />optimization tools can be applied. The eciency of the resulting strategies<br />is tested against two benchmarks representing common market practice on a<br />representative sample of real trading data.</p>

<p> Algoritamsko trgovanje je automatizovani proces izvr&scaron;avanja naloga<br /> na elektronskim berzama (berzama akcija). Osnovni cilj u izvr&scaron;enju je postizanje<br /> najefikasnije cene. Ovde su predložene dve optimalne strategije za<br /> izvr&scaron;enje atomskih naloga zasnovane na minimizaciji tro&scaron;kova impakta i volatilnosti u slučaju jednog trži&scaron;ta i vi&scaron;e trži&scaron;ta. Prva posmatrana strategija je<br /> zasnovana na relativno jednostavnom nelinearnom optimizacionom modelu,<br /> dok druga dozvoljava reoptimizaciju u nekom trenutku unutar zadatog vremenskog intervala izvr&scaron;enja. Konačno, posmatran je model koji dozvoljava<br /> reoptimizaciju u okruženju sa vi&scaron;e trži&scaron;ta. U svim slučajevima koristi se<br /> kombinacija market i limit naloga. Glavna inovacija u na&scaron;em pristupu je<br /> uvodjenje Fill Probability funkcije koja omogućava kombinaciju market i<br /> limit naloga u sva četiri modela diskutovana u ovoj tezi. Pod određenim<br /> uslovima funkcije cilja svih posmatranih problema su konveksne te se mogu<br /> primeniti standardni metodi optimizacije. Efikasnost predloženih strategija<br /> je testirana u odnosu na dve reprezentativne strategije, koje predstavljaju<br /> uobičajenu praksu, na realnom uzorku podataka sa trži&scaron;ta.</p>