Price signatures

Price signatures are statistical measurements that aim to detect systematic patterns in price dynamics localised around the point of trade execution. They are particularly useful in electronic trading because they uncover market dynamics, strategy characteristics, implicit execution costs, or counter-party trading behaviours that are often hard to identify, in part due to the vast amounts of data involved and the typically low signal to noise ratio. Because the signature summarises price dynamics over a specified time interval, it constitutes a curve (rather than a point estimate) and because of potential overlap in the price paths it has a non-trivial dependence structure which complicates statistical inference. In this paper, I show how recent advances in functional data analysis can be applied to study the properties of these signatures. To account for data dependence, I analyse and develop resampling-based bootstrap methodologies that enable reliable statistical inference and hypothesis testing. I illustrate the power of this approach using a number of case studies taken from a live trading environment in the over-the-counter currency market. I demonstrate that functional data analysis of price signatures can be used to distinguish between internalising and externalising liquidity providers in a highly effective data driven manner. This in turn can help traders to selectively engage with liquidity providers whose risk management style best aligns with their execution objectives.