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## Author

Listed:
• Jean Jacod
• Viktor Todorov

## 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.

## Suggested Citation

• Jean Jacod & Viktor Todorov, 2010. "Do price and volatility jump together?," Papers 1010.4990, arXiv.org.
• Handle: RePEc:arx:papers:1010.4990
as

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

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