arXiv:2507.23646v4 Announce Type: replace Abstract: We develop the information geometry of L\'evy processes. The $\alpha$-divergence is derived directly in terms of the L\'evy triplets, and the corresponding Fisher information matrix and $\alpha$-connection are obtained from it. Potential functions and dually flat structures for a class of parametric L\'evy processes are also investigated. In addition, we discuss statistical implications of this information geometry, including bias reduction and Bayesian predictive priors. Several L\'evy processes widely used in financial modeling, such as tempered stable processes, the CGMY model, variance gamma processes, and the Merton model, are investigated as illustrative examples.