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MS Thesis Defence

Title: Asymmetric Super-Heston-rough volatility model with Zumbach effect as a scaling limit of quadratic Hawkes processes
Speaker: Priyanka Chudasama (IISc Mathematics)
Date: 06 October 2022
Time: 11 am
Venue: Hybrid - Microsoft Teams (online) and LH-3, 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 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 macro-scale, we introduce the bivariate Modified-quadratic Hawkes 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.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 15 Jul 2024