Lévy interest rate models with a long memory

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

No 2021020, LIDAM Discussion Papers 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: Finance; interest rate; Lévy process; Mittag-Leffler function; mean reverting process (search for similar items in EconPapers)
Date: 2021-01-01
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvad:2021020

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