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Erscheinungsjahr: 
2021
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[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 10 [Issue:] 1 [Article No.:] 2 [Publisher:] MDPI [Place:] Basel [Year:] 2022 [Pages:] 1-28
Verlag: 
MDPI, Basel
Zusammenfassung: 
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.
Schlagwörter: 
interest rate
Lévy process
Mittag&#x2013
Leffler function
mean reverting process
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