A0413
Title: Modelling financial volatility with quadratic Hawkes
Authors: Cecilia Aubrun - Ecole Polytechnique (France) [presenting]
Jean-Philippe Bouchaud - Capital Fund Management (France)
Michael Benzaquen - Ecole Polytechnique (France)
Abstract: Hawkes processes have been used in various fields, from seismology to finance to model endogenous dynamics. Those stochastic processes are particularly well suited to the problem because the feedback effect is explicitly described via a kernel that weights the influence of past events on the frequency of occurrence of future events. Non-linear extensions of Hawkes processes allow one to combine both excitatory and inhibitory effects and can describe an even broader range of phenomena: brain function, financial markets activity and volatility, and seismologic activity. Financial markets offer a prolific playground to study non-linear Hawkes. One special class of such non-linear processes, called quadratic Hawkes, was introduced and studied to model price movements. On top of the standard Hawkes feedback, a signed process (price changes in this context) also contributes to the current activity rate in a quadratic way. QHawkes is particularly interesting because it allows us to reproduce the stylized facts of financial time series: clustering of activity, fat-tailed distribution of financial returns, and time asymmetry. When considering several assets, one observes additional stylized facts: cross feedback effects between several financial products (cross leverage and Zumbach effects) and simultaneous price jumps of several assets, co-jumps. Considering those, we generalize the QHawkes by extending it in multi-dimensions.
