Continuous time analysis of fleeting discrete price moves
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 càdlàg 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2014
- DOI:
- 10.48550/arXiv.1410.7317
- arXiv:
- arXiv:1410.7317
- Bibcode:
- 2014arXiv1410.7317S
- Keywords:
-
- Quantitative Finance - Trading and Market Microstructure;
- Mathematics - Probability;
- 91G70 (Primary);
- 60G60 (Secondary)
- E-Print:
- 39 pages, 12 figures, \baselineskip=20pt, submitted to "Journal of the American Statistical Association"