Testing for jumps when asset prices are observed with noise–a “swap variance” approach

This paper proposes a new test for jumps in asset prices that is motivated by the literature on variance swaps. Formally, the test follows by a direct application of Itô’s lemma to the semi-martingale process of asset prices and derives its power from the impact of jumps on the third and higher order return moments. Intuitively, the test statistic reflects the cumulative gain of a variance swap replication strategy which is known to be minimal in the absence of jumps but substantial in the presence of jumps. Simulations show that the jump test has nice properties and is generally more powerful than the widely used bi-power variation test. An important feature of our test is that it can be applied–in analytically modified form–to noisy high frequency data and still retain power. As a by-product of our analysis, we obtain novel analytical results regarding the impact of noise on bi-power variation. An empirical illustration using IBM trade data is also included.