A mutually exciting rough jump-diffusion for financial modelling

Donatien Hainaut ()
Additional contact information
Donatien Hainaut: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2024002, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: This article introduces a new class of diffusive processes with rough mutually exciting jumps for modeling financial asset returns. The novel feature is that the memory of positive and negative jump processes is defined by the product of a dampening factor and a kernel involved in the construction of the rough Brownian motion. The jump processes are nearly unstable because their intensity diverges to +[infinite] for a brief duration after a shock. We first infer the stability conditions and explore the features of the dampened rough (DR) kernel, which defines a fractional operator, similar to the Riemann-Liouville integral. We next reformulate intensities as infinite-dimensional Markov processes. Approximating these processes by discretization and then considering the limit allows us to retrieve the Laplace transform of asset log-return. We show that this transform depends on the solution of a particular fractional integro-differential equation. We also define a family of changes of measure that preserves the features of the process under a risk-neutral measure. We next develop an econometric estimation procedure based on the peak over threshold (POT) method. To illustrate this work, we fit the mutually exciting rough jump-diffusion to time series of Bitcoin log-returns and compare the goodness of fit to its non-rough equivalent. Finally, we analyze the influence of roughness on option prices.

Keywords: Self-exciting process; Epidemic Type Aftershock Sequence (ETAS); jump-di􏰀ffusion; fractional Brownian motion; Riemann-Liouville fractional integral (search for similar items in EconPapers)
Pages: 29
Date: 2024-01-12
Note: In: Fractional Calculus and Applied Analysis, 2024, vol. 27(1), p. 319-352
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

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:louvar:2024002

DOI: 10.1007/s13540-023-00234-4

Access Statistics for this paper

More papers in LIDAM Reprints 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 ().