Lévy Interest Rate Models with a Long Memory
(2022) Risks — Vol. 10, n° 1, p. 2 (2022)
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- 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.
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Citations
Hainaut, D. (2022). Lévy Interest Rate Models with a Long Memory. Risks, 10(1), 2. https://doi.org/10.3390/risks10010002 (Original work published 2022)