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Lévy Processes and Extreme Value Theory


There are fundamentally two different ways of viewing the uncertainty of financial asset prices in continuous time. The first assumes the principle of continuity, the second does not. This chapter develops the relationships connecting the Levy processes and extreme value theory (EVT). It begins by defining the modeling alternative and the challenges contemporary finance has to tackle. Next, the chapter presents the link with EVT. It talks about the main definitions of the EVT framework. Then, it moves to a presentation of Lévy processes and studies stable Lévy processes. The chapter examines two subclasses of semi-heavy-tailed Lévy processes that are based on tempered stable and generalized hyperbolic distributions. Finally, the chapter deals with the relationships between Lévy processes and extreme value distributions. It also studies the Fisher-Tippett theorem, Generalized Jenkinson-von Mises distribution, and maximum domains of attraction.
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hal-04561146 , version 1 (26-04-2024)




Christian Walter, Olivier Le Courtois. Lévy Processes and Extreme Value Theory. François Longin. Extreme Events in Finance: A Handbook of Extreme Value Theory and its Applications, 1, John Wiley and Sons, 2016, 9781118650196. ⟨10.1002/9781118650318.ch8⟩. ⟨hal-04561146⟩
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