Estimation of continuous-time financial models using high-frequency data [Elektronische Ressource] / vorgelegt von Christian Pigorsch

Estimation of Continuous–TimeFinancial Models UsingHigh–Frequency DataDissertation an der Fakulta¨t fu¨r Mathematik, Informatik und Statistik derLudwig-Maximilians-Universit¨at Mu¨nchenvorgelegt vonChristian Pigorsch am 1. Februar 2007Ludwig-Maximilians-Universita¨t Mu¨nchenFakulta¨t fu¨r Mathematik, Informatik und StatistikDissertationEstimation of Continuous–TimeFinancial Models UsingHigh–Frequency Datavorgelegt vonChristian PigorschMu¨nchen, den 1. Februar 2007Erstgutachter: Prof. Stefan Mittnik, Ph.D.Zweitgutachter: Prof. Dr. Ludwig FahrmeirExterner Gutachter: Prof. A. Ronald Gallant, Ph.D.Rigorosum: 5. Juni 2007Contents1 Introduction 82 High–Frequency Information 112.1 Definition of Realized Variation and Covariation Measures . . . . . 122.1.1 Realized Variation . . . . . . . . . . . . . . . . . . . . . . . 142.1.2 Realized Covariation . . . . . . . . . . . . . . . . . . . . . . 162.2 Stylized Facts of Returns and Realized Variation Measures . . . . . 172.2.1 Univariate Dataset . . . . . . . . . . . . . . . . . . . . . . . 172.2.2 Multivariate Dataset . . . . . . . . . . . . . . . . . . . . . . 243 StatisticalAssessmentofUnivariateContinuous–TimeStochasticVolatil-ity Models 363.1 Model Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . 373.1.1 Affine Models . . . . . . . . . . . . . . . . . . . . . . . . . . 383.1.2 Logarithmic Models. . . . . . . . . . . . . . . . . . . . . . . 393.1.3 Jump–Diffusion Models . . . . . . . . .