A fractional Hawkes process for illiquidity modeling

The Amihud illiquidity measure has proven to be very popular in the economic and financial literature for measuring the illiquidity process of stocks and indices. None of the existing discrete-time illiquidity models in the literature are however adapted for reproducing peaks of illiquidity with long memory and for the management of the liquidity risk associated with these securities. This paper therefore proposes a new continuous-time paradigm for modeling illiquidity via a novel fractional Hawkes process in which the intensity process is ruled by a modified Mittag-Leffler excitation function. By considering a mean-reverting jump-diffusion model for the (log-)Amihud measure where jumps follow this modified fractional Hawkes process, we then manage to effectively reproduce the observed peaks of illiquidity in financial markets while introducing long-term effects and tractability in the model. We can therefore use this model to directly perform risk management on the Amihud illiquidity measure. This paper hence provides new tools for a better management of the illiquidity risk in financial markets.