Stationary Increment Tempered Fractional Lévy Processes (TFLP) introduced by Boniece, Didier and Sabzikar (2020) are applied to financial data. They are used to model the stochastic drift rate of a mean reverting equation. The new processes are called OU processes with a TFLP drift rate....

Observing prices of European put and call options, we calibrate exponential Lévy models nonparametrically. We discuss the implementation of the spectral estimation procedures for Lévy models of finite jump activity as well as for self-decomposable Lévy models and improve these methods....