Lévy Interest Rate Models with a Long Memory

Donatien Hainaut
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Donatien Hainaut: UCLouvain, LIDAM, Louvain-La-Neueve, 1348 Ottignies-Louvain-la-Neuve, Belgium

Risks, 2021, vol. 10, issue 1, 1-28

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)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:10:y:2021:i:1:p:2-:d:709975

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