15:15  Prof. Alexander Schnurr (Siegen): The fourth characteristic of a semimartingale

We extend the class of semimartingales in a natural way. This allows us to incorporate processes having paths that leave the state space R^d. By carefully distinguishing between two killing states, we are able to introduce a fourth semimartingale characteristic which generalizes the fourth part of the Levy quadruple. Using the probabilistic symbol, we analyze the close relationship between the generators of certain Markov processes with killing and their (now four) semimartingale characteristics

16:45 Prof. Markus Bibinger (Marburg): Statistical analysis of path properties of volatility

In this talk, we review recent contributions on statistical theory to infer path properties of volatility. The interest is in the latent volatility of an Itô semimartingale, the latter being discretely observed over a fixed time horizon.We consider tests to discriminate continuous paths from paths with volatility jumps. Both a local test for jumps at specified times and a global test for jumps over the whole observation interval are discussed. We establish consistency and optimality properties under infill asymptotics, also for observations with additional additive noise. Recently, there is high interest in the smoothness regularity of the volatility process as conflicting models are proposed in the literature. To address this point, we consider inference on the Hurst exponent of fractional stochastic volatility processes. Even though the regularity of the volatility determines optimal spot volatility estimation methods, forecasting techniques and the volatility persistence, its identifiability is one of the few unsolved questions in high-frequency statistics. We discuss a first approach which can reveal if path properties are stable over time or changing. Eventually, we discuss some recent considerations and conjectures on this open question.