Nonparametric Tests for Analyzing the Fine Structure of Price Fluctuations

Columbia University Financial Engineering Report No. 2007-13

35 Pages Posted: 11 Jan 2008 Last revised: 30 May 2014

See all articles by Rama Cont

Rama Cont

University of Oxford

Cecilia Mancini

University of Florence - Department of management and economics

Date Written: November 2007

Abstract

We consider a semimartingale model where (the logarithm of) an asset price is modeled as the sum of a Levy process and a general Brownian semimartingale. Using a nonparametric threshold estimator for the continuous component of the quadratic variation (integrated variance), we design a test for the presence of a continuous component in the price process and a test for establishing whether the jump component has finite or infinite variation based on observations on a discrete time grid. Using simulations of stochastic models commonly used in finance, we confirm the performance of our tests and compare them with analogous tests constructed using multipower variation estimators of integrated variance. Finally, we apply our tests to investigate the fine structure of the DM/USD exchange rate process and of SPX futures prices. In both cases, our tests reveal the presence of a non-zero Brownian component, combined with a finite variation jump component.

Keywords: financial econometrics, jumps, exchange rates, high-frequency data, time series

JEL Classification: C14, C12, C22

Suggested Citation

Cont, Rama and Mancini, Cecilia, Nonparametric Tests for Analyzing the Fine Structure of Price Fluctuations (November 2007). Columbia University Financial Engineering Report No. 2007-13. Available at SSRN: https://ssrn.com/abstract=1081491 or http://dx.doi.org/10.2139/ssrn.1081491

Rama Cont (Contact Author)

University of Oxford ( email )

Mathematical Institute
Oxford, OX2 6GG
United Kingdom

HOME PAGE: http://https://www.maths.ox.ac.uk/people/rama.cont

Cecilia Mancini

University of Florence - Department of management and economics ( email )

via delle Pandette 9
Firenze, I-50127
Italy

HOME PAGE: http://www.unifi.it/index.php?module=ofform2&mode=2&cmd=1&AA=2013&dip=200052&ord=&doc=3f2a3d30352b30

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