Stationary generalized Ornstein-Uhlenbeck processes and their applications in finance

Date

Dec 11, 2013

Time

5:00 PM - 6:00 PM

Speaker

Dr. Anita Behme

Affiliation

TU Dresden, Institut für Mathematische Stochastik, Eleonore-Trefftz-Gastprofessorin

Series

TUD Dresdner Mathematisches Seminar

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Description

Im Rahmen des Dresdner Mathematischen Seminars finden in diesem Semester eine Reihe von Eleonore-Trefftz-Vorlesungen statt, welche durch das Eleonore-Trefftz-Gastprofessorinnenprogramm der Exzellenzinitiative gefördert werden. By embedding an AR(1) time series with random coefficients into a continuous time setting, De Haan and Karandikar (1989) introduced the nowadays well-known generalized Ornstein-Uhlenbeck (GOU) process driven by a bivariate L\'evy process.In this talk we focus on the applications of the GOU process in finance: We introduce the COGARCH process, which is a continuous-time analogon of the ARCH/GARCH time-series introduced 1982 (and 1986 resp.) by Engle and Bollerslev. We discuss its advantages and drawbacks and observe that in the COGARCH model jump sizes in volatility and price exhibit a fixed deterministic relationship. As this is not very realistic, a multi-factor model is needed which can be provided by superpositions of the above model. Therefore we suggest one possible superposition of COGARCH (supCOGARCH) volatility processes driven by L\'evy bases and define the corresponding price processes. Some distributional properties of volatility and price will be shown. In particular we find that the supCOGARCH models allow for more flexible autocovariance structures than the COGARCH. Moreover, other than the COGARCH model and other financial volatility models, the supCOGARCH processes do not exhibit a deterministic relationship between jumps of price and volatility processes. Finally we present an extension of the GOU process to a multivariate setting and suggest how such multivariate GOU processes can again be used as squared volatilities in a COGARCH-like manner. This talk is based on joint works with Carsten Chong, Claudia Kl\"uppelberg and Alexander Lindner.

Links

• Dresdner Mathematisches Seminar
• Eleonore-Trefftz-Vorlesungen im Dresdner Mathematischen Seminar

Last modified: Dec 5, 2013, 12:52:01 PM