Hainaut, Donatien
[UCL]
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.
Bibliographic reference |
Hainaut, Donatien. Lévy interest rate models with a long memory. LIDAM Discussion Paper ISBA ; 2021/20 (2021) 29 pages |
Permanent URL |
http://hdl.handle.net/2078.1/245422 |