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Regular version of the site

Book chapter

Estimation and Calibration of Lévy Models via Fourier Methods

P. 1-76.
Belomestny D., Reiss M.

In this chapter we discuss different aspects of statistical estimation
for Lévy-based processes based on low-frequency observations. In particular, we
consider the estimation of the Lévy triplet and the Blumenthal-Getoor index in Lévy
and time-changed Lévy models. Moreover, a calibration problem in exponential
Lévy models based on option data is studied. The common feature of all these
statistical problems is that they can be conveniently formulated in the Fourier
domain. We introduce a general spectral estimation/calibration approach that can
be applied to these and many other statistical problems related to Lévy processes.
On the theoretical side, we provide a comprehensive convergence analysis of the
proposed algorithms and address each time the question of optimality.










In book

Belomestny D., Comte F., Genon-Catalot V. et al. Vol. 2128: Lévy Matters IV. Heidelberg: Springer, 2014.