Continuous-time methods in the study of discretely sampled functionals of Lévy processes. I. The positive process case

Citation
Schröder, Michael, Continuous-time methods in the study of discretely sampled functionals of Lévy processes. I. The positive process case, Advances in applied probability , 39(1), 2007, pp. 245-270
ISSN journal
00018678
Volume
39
Issue
1
Year of publication
2007
Pages
245 - 270
Database
ACNP
SICI code
Abstract
In this paper we develop a constructive approach to studying continuously and discretely sampled functionals of Lévy processes. Estimates for the rate of convergence of the discretely sampled functionals to the continuously sampled functionals are derived, reducing the study of the latter to that of the former. Laguerre reduction series for the discretely sampled functionals are developed, reducing their study to that of the moment generating function of the pertinent Lévy processes and to that of the moments of these processes in particular. The results are applied to questions of contingent claim valuation, such as the explicit valuation of Asian options, and illustrated in the case of generalized inverse Gaussian Lévy processes.