Lévy Interest Rate Models with a Long Memory

This article proposes an interest rate model ruled by mean reverting Lévy processes with a sub-exponential memory of their sample path. feature is achieved considering Ornstein–Uhlenbeck process in which the exponential decaying kernel replaced Mittag–Leffler function. Based on representation term infinite dimensional Markov processes, we present main characteristics bonds and short-term rates this setting. Their dynamics under risk neutral forward measures are studied. Finally, bond options valued discretization scheme discrete Fourier’s transform.