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FULL TITLE: Modelling and measuring slippage using the signature of order book data
We aim to explore how multiple features observed in real market data can be characterised quantitatively via a property of sample paths known as the signature of the path.
At an abstract mathematical level, the notion of a signature as an informative transform of a multidimensional time series was established by Ben Hambly and Terry Lyons , meanwhile Ni Hao et al  have introduced the possibility of its use to understand financial data and pointed to the power this approach has for machine learning and prediction.
We evaluate and refine these theoretical suggestions against some real world data and practical examples. Moreover, the paper identifies a low dimensional part of the signature that preserves essential information for understanding and measuring various market features in order to improve the efficient choice of trade execution algorithms.
 Ben Hambly, Terry Lyons, "Uniqueness for the signature of a path of bounded variation and the reduced path group", Annals of Mathematics, Pages[masked] from Volume 171 (2010), Issue 1
 Ni Hao, Daniel Levin and Terry Lyons - "Learning from the past, predicting the statistics for the future, learning an evolving system", preprint, 2012
Lajos Gergely Gyurko obtained a DPhil in Mathematics from the Mathematical Institute, University of Oxford. After graduating he joined the institute as a Departmental Lecturer. Beyond lecturing numerical methods, Greg is the course director of the Mathematical and Computational Finance MSc and faculty member of the Oxford-Man Institute of Quantitative Finance. Greg's research interests are Rough Paths Theory and its applications in Computational Finance.