Levy density estimation via information projection onto wavelet subspaces

Abstract

This paper proposes a nonparametric method for producing smooth and positive estimates of the density of a Levy process, which is widely used in mathematical finance. We use the method of logwavelet density estimation to estimate the Levy density with discretely sampled observations. Since Levy densities are not necessarily probability densities, we introduce a divergence measure similar to Kullback-Leibler information to measure the difference between two Levy densities. Rates of convergence are established over Besov spaces. (C) 2010 Elsevier B.V. All rights reserved.