Lévy Interest Rate Models with a Long Memory

Donatien Hainaut
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Donatien Hainaut: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2022001, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: This article proposes an interest rate model ruled by mean reverting Lévy processes with a sub-exponential memory of their sample path. This feature is achieved by considering an Ornstein–Uhlenbeck process in which the exponential decaying kernel is replaced by a Mittag–Leffler function. Based on a representation in term of an infinite dimensional Markov processes, we present the main characteristics of bonds and short-term rates in this setting. Their dynamics under risk neutral and forward measures are studied. Finally, bond options are valued with a discretization scheme and a discrete Fourier’s transform.

Keywords: Interest rate; Lévy process; Mittag-Leffler function; Mean reverting process (search for similar items in EconPapers)
Pages: 28
Date: 2022-01-01
Note: In: Risks, 2022, vol. 10(1), 2
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2022001

DOI: 10.3390/risks10010002

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