Nonparametric tests for pathwise properties of semimartingales

By Rama Cont, Cecilia Mancini. 2011

90 citations recorded by the source corpus.

We propose two nonparametric tests for investigating the pathwise properties of a signal modeled as the sum of a L\'evy process and a Brownian semimartingale. Using a nonparametric threshold estimator for the continuous component of the quadratic variation, we design a test for the presence of a continuous martingale component in the process and a test for establishing whether the jumps have finite or infinite variation, based on observations on a discrete time grid. We evaluate the performance of our tests using simulations of various stochastic models and use the tests to investigate the fine structure of the DM/USD exchange rate fluctuations and SPX futures prices. In both cases, our tests reveal the presence of a non-zero Brownian component and a finite variation jump component.

Subfields: Applied Mathematics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/4a06626ba879beede7f72dafda15ee052308e94b

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In Applied Mathematics

In Finance

In Management Science and Operations Research

Citations in the corpus

Rough Volatility: Fact or Artefact? (2022, background): “Several empirical studies have attempted to estimate the roughness of ‘realized volatility’ signals using high-frequency data [1, 3, 11, 19, 24].”
IDENTIFYING THE BROWNIAN COVARIATION FROM THE CO-JUMPS GIVEN DISCRETE OBSERVATIONS (2012, methodology): “Although tests for the presence of co-jumps exist (Barndorff-Nielsen and Shephard, 2004b; Jacod and Todorov, 2009), by using our estimator of IC and extending the results in Cont and Mancini (2011) to a bivariate framework we could also test for the presence of Brownian components.”
Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data (2010, background): “Cont and Mancini (2011) use threshold or truncation-based estimators of the continuous component of the quadratic variation, originally proposed in Mancini (2001), in order to test for the presence of a continuous component in the price process.”
A CONSISTENT PRICING MODEL FOR INDEX OPTIONS AND VOLATILITY DERIVATIVES (2009, methodology): “Further statistical evidence that the jumps in the level of the S&P 500 index are accompanied by jumps of opposite sign in its volatility is provided by nonparametric tests for simultaneous jumps (Jacod and Todorov 2010; Todorov and Tauchen 2010).”