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

Rofeide Jabbari; Pablo Olivares

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arXiv · 2411.19192

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

Rofeide Jabbari·Pablo Olivares

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Abstract

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.

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Rofeide Jabbari, Pablo Olivares. 2024-11-28. Characteristic function and Esscher transform of a switching Levy model for the temperature dynamic. https://arxiv.org/abs/2411.19192

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