Title:
Nonparametric estimation for Levy processes with a view towards mathematical finance
Nonparametric estimation for Levy processes with a view towards mathematical finance
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Author(s)
Figueroa-Lopez, Enrique
Houdré, Christian
Houdré, Christian
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Abstract
Nonparametric methods for the estimation of the Levy density of a Levy process X are developed. Estimators that can be written
in terms of the "jumps" of X are introduced, and so are discrete-data based approximations. A model selection approach made up of
two steps is investigated. The first step consists in the selection of a
good estimator from a linear model of proposed Levy densities, while
the second is a data-driven selection of a linear model among a given
collection of linear models. By providing lower bounds for the minimax
risk of estimation over Besov Levy densities, our estimators are shown
to achieve the "best" rate of convergence. A numerical study for
the case of histogram estimators and for variance Gamma processes,
models of key importance in risky asset price modeling driven by Levy
processes, is presented.
Sponsor
NSF and NSA grants
Date Issued
2004-11
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Text
Resource Subtype
Pre-print