Do price and volatility jump together?

Abstract

We consider a process $X_t$, which is observed on a finite time interval $[0,T]$, at discrete times $0,{\Delta }_n,2{\Delta }_n,\dots .$ This process is an Itô 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.

Published in at http://dx.doi.org/10.1214/09-AAP654 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Testing for common arrivals of jumps for discretely observed multidimensional processes

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