Well-balanced Levy Driven Ornstein-Uhlenbeck Processes

Abstract

In this paper we introduce the well-balanced Lévy driven Ornstein-Uhlenbeck process as a moving average process of the form $X_t=\int \exp (-\lambda |t-u|)d{L}_u$. In contrast to Lévy 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.

arXiv comment16 pages, 2 figure