A New Test for Jumps in Asset Prices

This paper proposes a new test for the presence of jumps in asset prices. The test is derived from a direct application of Itô’s lemma to the semi-martingale process of asset prices. Intuitively, the proposed test measures the impact of jumps on the third and higher order return moments and is also directly related to the profit/loss function of a variance swap replication strategy. We derive its asymptotic distribution and perform extensive simulations to examine the finite sample properties. Compared to Barndorff-Nielsen and Shephard’s bi-power variation test, the test proposed in this paper has a faster rate of convergence to its asymptotic distribution and is more powerful in detecting jumps. Moreover, in the presence of i.i.d. market microstructure noise, we show that the jump test remains valid with a modified asymptotic variance that is derived in closed form.