Bypassing the truncation problem of truncated Lévy flights

Raul Matsushita, Sergio Da Silva, Regina Da Fonseca, Mateus Nagata

Physica A: Statistical Mechanics and its Applications 559 (2020) 125035

https://doi.org/10.1016/j.physa.2020.125035

We suggest a solution to the problem of truncation of truncated Lévy flights by deductively finding a power law between the truncation length and its standard deviation. We offer a generalization where the pdf of returns is left unknown, and its distributional moments are allowed to vary in time. Our model fits well with a financial dataset, which exhibits extreme moves.