The aim of this thesis is to estimate the volatility function of continuoustime stochastic models. The estimation of the volatility of the following wellknown international stock market indexes is presented as an application: Dow Jones Industrial Average, Standard and Poor’s 500, NIKKEI 225, CAC 40, DAX 30, FTSE 100 and IBEX 35. This estimation is studied from two different perspectives: a) assuming that the volatility of the stock market indexes displays shortrange dependence (SRD), and b) extending the previous model for processes with longrange dependence (LRD), intermediaterange dependence (IRD) or SRD. Under the efficient market hypothesis (EMH), the compatibility of the Vasicek, the CIR, the Anh and Gao, and the CKLS models with the stock market indexes is being tested. Nonparametric techniques are presented to test the affinity of these parametric volatility functions with the volatility observed from the data. Under the assumption of possible statistical patterns in the volatility process, a new estimation procedure based on the Whittle estimation is proposed. This procedure is theoretically and empirically proven. In addition, its application to the stock market indexes provides interesting results.

Thesis (M.Ch.E.)--University of Delaware, 2007. / Principal faculty advisors: Dionisios G. Vlachos and Babatunde Ogunnaike, Dept. of Chemical Engineering. Includes bibliographical references.

Thesis (Ph. D.)--University of New South Wales, 2002. / Also available online.

Thesis (Ph. D.)--Missouri University of Science and Technology, 2008. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed August 21, 2008) Includes bibliographical references (p. 124-131).

Thesis (Ph. D.)--University of Hong Kong, 2008. / Includes bibliographical references (leaf 151-160) Also available in print.

Thesis (M.Eng.). / Written for the Dept. of Civil Engineering and Applied Mechanics. Title from title page of PDF (viewed 2008/05/13). Includes bibliographical references.

Thesis (Ph.D.). / Written for the Dept. of Mathematics. Title from title page of PDF (viewed 2008/08/07). Includes bibliographical references.

Thesis (Ph.D) - Swinburne University of Technology, Faculty of Information & Communication Technologies, 2008. / [A thesis submitted in total fulfillment of the requirements of for the degree of Doctor of Philosophy, Faculty of Information and Communication Technologies, Swinburne University of Technology, 2008]. Typescript. Includes bibliographical references p. 193-201.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2008. / Includes bibliographical references (leaves 168-176). Also available in electronic version.

Thesis (Ph.D.) - University of Glasgow, 2008. / Ph.D. thesis submitted to the Faculty of Information and Mathematical Sciences, Department of Statistics, 2008. Includes bibliographical references. Print version also available.