Mathematics Colloquium | Aditi Dandapani
March 5 @ 10:00 am - 11:00 am
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Title: From Quadratic Hawkes Processes to Super Heston Rough Volatility
Abstract: Using microscopic price models based on Hawkes processes, it has been shown that under some no-arbitrage conditions, the high degree of endogeneity of markets together with the phenomenon of metaorders splitting generates rough Heston-type volatility at the macroscopic scale. One additional important feature of financial dynamics, at the heart of several influential works in econophysics, is the so-called feedback or Zumbach effect. This essentially means that past trends in returns convey significant information on future volatility. A natural way to reproduce this property in microstructure modeling is to use quadratic versions of Hawkes processes. We show that after suitable rescaling, the long-term limits of these processes are refined versions of rough Heston models where the volatility coefficient is enhanced compared to the square root characterizing Heston-type dynamics. Furthermore, the Zumbach effect remains explicit in these limiting rough volatility models.