Advances in High Frequency Strategies

Abstract

This doctoral dissertation, in the field of Mathematical Finance, has received Complutense University-s Ph.D. Prize for the academic year 2011/2012. It is also the author s second Ph.D. dissertation. His first Ph.D.s dissertation was in the field of Financial Economics, and was published in 2003 (https www.educacion.gob.es/teseo/mostrarRef.do ref 295773).Recent legislative changes in the United States (RegNMS) and Europe (MiFID), preceded by substantial technological advances in computation and communication, have been conducive to the proliferation of high frequency trading strategies. About 70 por ciento of the total transacted volume in stocks has been estimated to originate from high frequency operators. In futures markets, that figure is believed to exceed 50%. The goal of this doctoral dissertation is to examine, from a mathematical perspective, how market microstructure theories need to be adjusted to the new high frequency trading framework. Chapter I explains that current market participants follow a volume or transactional clock, as opposed to operating in chronological time. Much of market microstructure theory is built upon the paradigm of chronological time, and must therefore be re-formulated. Our approach generalizes the PIN Theory of Easley and O Hara (1996), by proposing a new estimate of the Probability of Informed Trading based on volume-time sampling, thus consistent with a high-frequency setting. Chapter II demonstrates that returns- volatility is partially caused by order flow toxicity, and that sampling order imbalance in volume-clock has predictive power over that toxicity-induced volatility.Chapter III shows that volume-time order imbalance reached an extreme value two hours before the May 6th 2010 flash crash, and that da-s 10 por ciento price plunge is likely to be the consequence of a liquidity crisis triggered by order flow toxicity.