A fractional Hawkes process for illiquidity modeling

Jean-Loup Dupret () and Donatien Hainaut ()
Additional contact information
Jean-Loup Dupret: Université catholique de Louvain, LIDAM/ISBA, Belgium
Donatien Hainaut: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2023001, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: The Amihud illiquidity measure has proven to be very popular in the empirical literature for measuring the illiquidity process of stocks and indices. Many econometric models in discrete time have then been proposed for this Amihud measure. Such models are however not adapted for reproduc- ing peaks of illiquidity with long-memory, for risk management and for pricing liquidity-related derivatives. This paper therefore proposes a new paradigm for modeling illiquidity via a continuous- time process with jumps exhibiting long-range dependence. More precisely, we first introduce a new fractional Hawkes process in which the intensity process is ruled by a modified Mittag-Leffler excitation function. Working with a mean-reverting jump model for the (log-)Amihud measure where jumps follow this modified fractional Hawkes process then allows to easily reproduce the observed peaks of illiquidity in financial markets while introducing long-range dependence and tractability in the model. Indeed, thanks to this modified Mittag-Leffler kernel, we show that our model for the (log)-Amihud measure admits a characteristic function in semi-closed form while having a long-memory of past events, which is not achievable with the existing Hawkes processes. We can therefore use this model to perform risk management on illiquidity as well as to introduce and price illiquidity derivatives on the Amihud measure. We hence provide with this paper new tools for a better understanding and management of the illiquidity risk in financial markets.

Keywords: Illiquidity modeling; Amihud measure; Hawkes process; Mittag-Leffler function; Illiquidity derivatives; Risk management (search for similar items in EconPapers)
Pages: 40
Date: 2023-01-01
New Economics Papers: this item is included in nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://dial.uclouvain.be/pr/boreal/en/object/bore ... tastream/PDF_01/view (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvad:2023001

Access Statistics for this paper

More papers in LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA) Voie du Roman Pays 20, 1348 Louvain-la-Neuve (Belgium). Contact information at EDIRC.
Bibliographic data for series maintained by Nadja Peiffer ().