Testing for uncorrelation or for a functional relationship between price and volatility jumps

Many continuous-time stochastic volatility models exhibit certain functional relationships between jumps in the price and volatility. These relations allow for the construction of tests and, hence, to test these models for high-frequency data. We present such tests in a fairly general context and derive some of their properties. We investigate their behavior in a simulation study. Finally we apply our tests to three data sets. It turns out that all models are rejected during most time periods. A similar test for no correlation of jumps in prices and volatilities cannot be rejected. This sheds new light on economically motivated statements on causality between jumps in prices and volatilities. MSC2010 Subject Classification: Primary 62F03, 62M02 Secondary 60H10, 60J60