A Generalized Bivariate Ornstein-Uhlenbeck Model for Financial Assets

• Main Authors: Krämer, Romy, Richter, Matthias
• Other Authors: TU Chemnitz, Fakultät für Mathematik
• Format: Others
• Language: English
• Published: Universitätsbibliothek Chemnitz 2008
• Subjects: Black-Scholes formula; financial analysis; generalized Ornstein-Uhlenbeck process; hedging; option pricing; ddc:510; Black-Scholes-Modell; Optionspreistheorie
• Online Access: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800572; http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800572; http://www.qucosa.de/fileadmin/data/qucosa/documents/5577/data/t_06_kr_ri.pdf; http://www.qucosa.de/fileadmin/data/qucosa/documents/5577/20080057.txt

In this paper, we study mathematical properties of a generalized bivariate Ornstein-Uhlenbeck model for financial assets. Originally introduced by Lo and Wang, this model possesses a stochastic drift term which influences the statistical properties of the asset in the real (observable) world. Furthermore, we generali- ze the model with respect to a time-dependent (but still non-random) volatility function. Although it is well-known, that drift terms - under weak regularity conditions - do not affect the behaviour of the asset in the risk-neutral world and consequently the Black-Scholes option pricing formula holds true, it makes sense to point out that these regularity conditions are fulfilled in the present model and that option pricing can be treated in analogy to the Black-Scholes case.