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Krämer, Romy; Richter, Matthias : A Generalized Bivariate Ornstein-Uhlenbeck Model for Financial Assets

Krämer, Romy ; Richter, Matthias : A Generalized Bivariate Ornstein-Uhlenbeck Model for Financial Assets

Author(s):
Krämer, Romy
Richter, Matthias
Title:
A Generalized Bivariate Ornstein-Uhlenbeck Model for Financial Assets
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 1, 2007
Mathematics Subject Classification:
60G15 [ Gaussian processes ]
60G44 [ Martingales with continuous parameter ]
91B28 [ Finance, portfolios, investment ]
Abstract:
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 generalize 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.
Keywords:
generalized Ornstein-Uhlenbeck process, option pricing, Black-Scholes formula
Language:
English
Publication time:
1 / 2007