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Simultaneous Confidence Statements about the Diffusion Coefficient of an Ito-Process with Application to Spot Volatility Estimation

dc.contributor.advisorMunk, Axel Prof. Dr.
dc.contributor.authorSabel, Till
dc.date.accessioned2014-07-28T09:33:27Z
dc.date.available2014-07-28T09:33:27Z
dc.date.issued2014-07-28
dc.identifier.urihttp://hdl.handle.net/11858/00-1735-0000-0022-5F35-2
dc.identifier.urihttp://dx.doi.org/10.53846/goediss-4610
dc.identifier.urihttp://dx.doi.org/10.53846/goediss-4610
dc.language.isoengde
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/
dc.subject.ddc510de
dc.titleSimultaneous Confidence Statements about the Diffusion Coefficient of an Ito-Process with Application to Spot Volatility Estimationde
dc.typedoctoralThesisde
dc.contributor.refereeMunk, Axel Prof. Dr.
dc.date.examination2014-07-16
dc.description.abstractengIn this PhD thesis, we address the problem of giving simultaneous confidence statements about local features of the diffusion of an Itô process. To this end, we construct a multiscale test based on weighted quadratic variation and prove that the test statistic can be strongly approximated by a sequence of Gaussian martingales which are distribution-free. Further, we give optimality results and present different visualization methods. In the second part of the thesis, we extend the approach to data corrupted by additive noise to cover applications from high-frequency finance. Additionally, we show which difficulties arise from real data and apply our method exemplarily to prices of Euro-Bund-Futures (FGBL). As an outlook for future work, we present ideas of generalizing the method to inference on the local covariance and point out some interesting applications from finance.de
dc.contributor.coRefereeDümbgen, Lutz Prof. Dr.
dc.subject.engnonparametric statistics; multiscale testing; volatility estimationde
dc.identifier.urnurn:nbn:de:gbv:7-11858/00-1735-0000-0022-5F35-2-4
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematics (PPN61756535X)de
dc.identifier.ppn791336395


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