Do price and volatility jump together

By Jean Jacod, V. Todorov. 2010

121 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/af67773425733d8ce50a971a8d7cbd804604c01f

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Citations in the corpus

Resolution of Policy Uncertainty and Sudden Declines in Volatility (2017, unknown): “…and disentangle from Brownian shocks generated by stochastic volatility at a daily frequency.9 Second, if the intensities of Poisson jumps are independent for Y and X , then there would be no co-jumps of Y and X almost surely, which conflicts with the data, see, e.g., Jacod and Todorov (2010).”
Multivariate supOU processes (2010, background): “It should be noted that in this model jumps in the price and the volatility always occur together which is reasonable for financial data (see [25]).”
Self-Exciting Jumps, Learning, and Asset Pricing Implications (2015, background): “…convexity adjustment term is kJ(1)T2,t = ( k+J (1) + k − J (1) ) T2,t. Recent empirical studies find that a big negative jump in asset prices tends to be associated with an abrupt move in asset variance, i.e., co-jumps of prices and volatility (Jacod and Todorov, 2010; Todorov and Tauchen, 2011).”
Estimation of integrated volatility of volatility with applications to goodness-of-fit testing (2011, background): “recent work by Jacod and collaborators on the existence and the form of joint jumps in both processes (see [24] and [21]).”
Estimating the Spot Covariation of Asset Prices—Statistical Theory and Empirical Evidence (2014, unknown): “Assumption 2 depends on the smoothness parameter α and reads similar as Assumption (K-v) in Jacod and Todorov (2010).”