Characteristic function and Esscher transform of a switching Levy model for the temperature dynamic

In this paper we extend models for the dynamic of the temperatures by considering random switching between Levy noises instead of Brownian motions, with a mean-reverting movement towards a seasonal periodic function. The use of Levy noises allows for jumps, capturing, together with the regime changes, sudden and relatively persistent oscillations in the weather. An approximated close-form expression for the characteristic function of the temperature process under an Esscher transform is given.