Abstract
We consider a semimartingale model where (the logarithm of) an asset price is modeled as the sum of a Levy process and a general Brownian semimartingale. Using a nonparamet- ric threshold estimator for the continuous component of the quadratic variation (integrated variance), we design • a test for the presence of a continuous component in the price process • a test for establishing whether the jump component has finite or infinite variation based on observations on a discrete time grid. Using simulations of stochastic models com- monly used in finance, we confirm the performance of our tests and compare them with anal- ogous tests constructed using multipower variation estimators of integrated variance. Finally, we apply our tests to investigate the fine structure of the DM/USD exchange rate process and of SPX futures prices. In both cases, our tests reveal the presence of a non-zero Brownian component, combined with a finite variation jump component.
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