Do price and volatility jump together?

TL;DR

This paper develops statistical tests to determine whether jumps in a financial process's price and volatility occur simultaneously, providing methods with proven asymptotic properties and demonstrating their effectiveness on real market data.

Contribution

It introduces two families of tests for detecting common versus disjoint jumps in price and volatility processes with asymptotic level guarantees.

Findings

Tests perform well in simulations

Tests successfully applied to S&P 500 data

Method distinguishes between common and disjoint jumps

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.