Well-balanced Levy Driven Ornstein-Uhlenbeck Processes

Details Well-balanced Levy Driven Ornstein-Uhlenbeck Processes Well-balanced Levy Driven Ornstein-Uhlenbeck Processes

2010-12-03

arxiv.org/abs/1012.0691v2

Mathematics

Probability

16 pages, 2 figure

Scientific paper

In this paper we introduce the well-balanced L\'{e}vy driven Ornstein-Uhlenbeck process as a moving average process of the form $X_t=\int \exp(-\lambda |t-u|)dL_u$. In contrast to L\'{e}vy driven Ornstein-Uhlenbeck processes the well-balanced form possesses continuous sample paths and an autocorrelation function which is decreasing not purely exponential but of the order $\lambda |u|\exp(-\lambda |u|)$. Furthermore, depending on the size of $\lambda$ it allows both for positive and negative correlation of increments. We indicate how the well-balanced Ornstein-Uhlenbeck process might be used as mean or volatility process in stochastic volatility models.

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