A New Test for Jumps in Asset Prices

Abstract

This paper proposes a new test for the presence of jumps in asset prices. The test is derived from a di-rect 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 dis-tribution 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.

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