Title: Asymmetric Super-Heston-rough volatility model with Zumbach effect as a scaling limit of quadratic Hawkes processes
Speaker: Priyanka Chudasama (IISc Mathematics)
Date: 30 March 2022
Time: 11 am
Venue: LH-1, Mathematics Department
Modelling price variation has always been of interest, from options pricing to risk management.
It has been observed that the high-frequency financial market is highly volatile, and the
volatility is rough. Moreover, we have the Zumbach effect, which means that past trends in the
price process convey important information on future volatility. Microscopic price models based
on the univariate quadratic Hawkes (hereafter QHawkes) process can capture the Zumbach effect
and the rough volatility behaviour at the macroscopic scale. But they fail to capture the
asymmetry in the upward and downward movement of the price process. Thus, to incorporate
asymmetry in price movement at micro-scale and rough volatility and the Zumbach effect at
macroscale, we introduce the bivariate Modified-QHawkes process for upward and downward price
movement. After suitable scaling and shifting, we show that the limit of the price process in
the Skorokhod topology behaves as so-called Super-Heston-rough model with the Zumbach effect.