15:15 Uhr: Mark Podolskij (Aarhus): High frequency functionals of semimartingales: probabilistic results and statistical applications
In this talk we present a survey on asymptotic results for high frequency statistics of semimartingales that have been developed in the last twenty years. The theory originates from the work of Jean Jacod starting in the mid 90's and it received a lot of attention with the appearance of high frequency financial data. We will see why high frequency functionals lead to quite non-standard results both from probabilistic and statistical point of view, and try to understand the basic logic behind the limit theory.
16:45 Uhr: Mathieu Rosenbaum (Ecole Polytechnique, Paris): Rough Heston model: Pricing, hedging and microstructural foundations
It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities. However, due to the non-Markovian nature of the fractional Brownian motion, they raise new issues when it comes to the risk management of derivatives. Using an original link between nearly unstable Hawkes processes and rough volatility models, we explain in this talk how to price and hedge options in the rough version of the Heston model.
This is joint work with Omar El Euch.
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