Continuous time analysis of fleeting discrete price moves

TL;DR

This paper introduces a new continuous-time, discrete-price model for financial markets that captures rapid reversals in price movements and fits high-frequency data effectively.

Contribution

It presents an analytically tractable model of discrete, continuous-time prices with rapid reversals, fitting high-frequency futures data across multiple time scales.

Findings

Model accurately describes price dynamics over various time scales

Fits four high-frequency futures data sets well

Captures rapid price reversals in financial markets

Abstract

This paper proposes a novel model of financial prices where: (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically tractable and directly formulated in terms of the calendar time and price impact curve. The resulting c\`{a}dl\`{a}g price process is a piecewise constant semimartingale with finite activity, finite variation and no Brownian motion component. We use moment-based estimations to fit four high frequency futures data sets and demonstrate the descriptive power of our proposed model. This model is able to describe the observed dynamics of price changes over three different orders of magnitude of time intervals.