Lévy density estimation via information projection onto wavelet subspaces

This paper proposes a nonparametric method for producing smooth and positive estimates of the density of a Lévy process, which is widely used in mathematical finance. We use the method of logwavelet density estimation to estimate the Lévy density with discretely sampled observations. Since Lévy densities are not necessarily probability densities, we introduce a divergence measure similar to Kullback–Leibler information to measure the difference between two Lévy densities. Rates of convergence are established over Besov spaces.