Power-law intensity distributions in nonlinear Hawkews processes

Abstract

The Hawkes process is a flexible and versatile model that can accommodate the self-exciting nature of occurrences of events in natural and social sciences. Recently, a nonlinear version of this model has been applied to describe financial markets' intermittent and clustering behaviour. On the other hand, analytical characters of the nonlinear Hawkes process have not been studied well due to its nonlinear and non-Markovian nature. In this talk, we present our solution to a broad class of nonlinear Hawkes processes via the field master equations based on our previous publications (K. Kanazawa and D. Sornette, PRL 2020 and PRL 2021). We find that the power-law relationship is ubiquitously found in the intensity distributions in nonlinear Hawkes processes. This character would be helpful for data calibration to financial data, particularly from the viewpoint of the power-law price movement statistics.