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Do price and volatility jump together?

  • Jean Jacod
  • Viktor Todorov
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    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
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    Paper provided by arXiv.org in its series Papers with number 1010.4990.

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    Date of creation: Oct 2010
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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
    Contact details of provider: Web page: http://arxiv.org/

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