# Do price and volatility jump together?

## Author Info

• Jean Jacod
• Viktor Todorov
Registered author(s):

## Abstract

We consider a process $X_t$, which is observed on a finite time interval $[0,T]$, at discrete times $0,\Delta_n,2\Delta_n,\ldots.$ This process is an It\^{o} semimartingale with stochastic volatility $\sigma_t^2$. Assuming that $X$ has jumps on $[0,T]$, we derive tests to decide whether the volatility process has jumps occurring simultaneously with the jumps of $X_t$. There are two different families of tests for the two possible null hypotheses (common jumps or disjoint jumps). They have a prescribed asymptotic level as the mesh $\Delta_n$ goes to $0$. We show on some simulations that these tests perform reasonably well even in the finite sample case, and we also put them in use on S&P 500 index data.

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File URL: http://arxiv.org/pdf/1010.4990

## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1010.4990.

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Publication status: Published in Annals of Applied Probability 2010, Vol. 20, No. 4, 1425-1469
Handle: RePEc:arx:papers:1010.4990

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Web page: http://arxiv.org/

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## Citations

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Cited by:
1. Ishida, I. & McAleer, M.J. & Oya, K., 2011. "Estimating the Leverage Parameter of Continuous-time Stochastic Volatility Models Using High Frequency S&P 500 VIX," Econometric Institute Research Papers EI 2011-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
2. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2012. "Parametric Inference and Dynamic State Recovery from Option Panels," Global COE Hi-Stat Discussion Paper Series gd12-266, Institute of Economic Research, Hitotsubashi University.
3. Almut Veraart, 2011. "How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps?," AStA Advances in Statistical Analysis, Springer, vol. 95(3), pages 253-291, September.
4. Andras Fulop & Junye Li & Jun Yu, 2012. "Investigating Impacts of Self-Exciting Jumps in Returns and Volatility: A Bayesian Learning Approach," Global COE Hi-Stat Discussion Paper Series gd12-264, Institute of Economic Research, Hitotsubashi University.
5. Chiarella, Carl & He, Xue-Zhong & Huang, Weihong & Zheng, Huanhuan, 2012. "Estimating behavioural heterogeneity under regime switching," Journal of Economic Behavior & Organization, Elsevier, vol. 83(3), pages 446-460.
6. Andras Fulop & Junye Li & Jun Yu, 2011. "Bayesian Learning of Impacts of Self-Exciting Jumps in Returns and Volatility," Working Papers CoFie-10-2011, Sim Kee Boon Institute for Financial Economics.
7. Worapree Maneesoonthorn & Catherine S. Forbes & Gael M. Martin, 2014. "Inference on Self-Exciting Jumps in Prices and Volatility using High Frequency Measures," Papers 1401.3911, arXiv.org.

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