Continuous Time Analysis of Fleeting Discrete Price Moves
35 Pages Posted: 10 Dec 2014
Date Written: December 7, 2014
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 the role of the calendar time can be explicitly understood. It is directly formulated in terms of the 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.
Keywords: integer-valued stochastic process, Lévy basis, Lévy process, trawl process, market microstructure, realized variance, variance signature plot
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