Diffusion covariation and co-jumps in bidimensional asset price processes with stochastic volatility and infinite activity Lévy jumps

Fabio Gobbi; Cecilia Mancini

doi:10.1117/12.724566

15 June 2007 Diffusion covariation and co-jumps in bidimensional asset price processes with stochastic volatility and infinite activity Levy jumps

Fabio Gobbi, Cecilia Mancini

Author Affiliations +

Proceedings Volume 6601, Noise and Stochastics in Complex Systems and Finance; 660111 (2007) https://doi.org/10.1117/12.724566
Event: SPIE Fourth International Symposium on Fluctuations and Noise, 2007, Florence, Italy

Abstract

In this paper we consider two processes driven by diffusions and jumps. The jump components are Levy processes and they can both have finite activity and infinite activity. Given discrete observations we estimate the covariation between the two diffusion parts and the co-jumps. The detection of the co-jumps allows to gain insight in the dependence structure of the jump components and has important applications in finance. Our estimators are based on a threshold principle allowing to isolate the jumps. This work follows Gobbi and Mancini (2006) where the asymptotic normality for the estimator of the covariation, with convergence speed &sqrt;h, was obtained when the jump components have finite activity. Here we show that the speed is &sqrt;h only when the activity of the jump components is moderate.

Citation Download Citation

Fabio Gobbi and Cecilia Mancini "Diffusion covariation and co-jumps in bidimensional asset price processes with stochastic volatility and infinite activity Levy jumps", Proc. SPIE 6601, Noise and Stochastics in Complex Systems and Finance, 660111 (15 June 2007); https://doi.org/10.1117/12.724566

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