Asymmetric COGARCH processes. (December 2014)

• Record Type: Journal Article
• Authors: Behme, Anita; Klüppelberg, Claudia; Mayr, Kathrin
• Is Part Of: Journal of applied probability. Volume 51:Number A(2014)
• Page Start: 161
• Page End: 173
• Publication Date: 2014-12
• Subjects: APCOGARCH, -- asymmetric power COGARCH, -- COGARCH, -- first-jump approximation, -- continuous-time GARCH, -- GJR-GARCH, -- GJR-COGARCH, -- maximum-likelihood estimation, -- high-frequency data, -- method of moments, -- stochastic volatility; 60G10, -- 60G51, -- 62M05, -- 62F10, -- 62M10, -- 90G70; 519.2
• DOI: 10.1239/jap/1417528473
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract : Financial data are as a rule asymmetric, although most econometric models are symmetric. This applies also to continuous-time models for high-frequency and irregularly spaced data. We discuss some asymmetric versions of the continuous-time GARCH model, concentrating then on the GJR-COGARCH model. We calculate higher-order moments and extend the first-jump approximation. These results are prerequisites for moment estimation and pseudo maximum likelihood estimation of the GJR-COGARCH model parameters, respectively, which we derive in detail.