Well-balanced Levy Driven Ornstein-Uhlenbeck Processes

In this paper we introduce the well-balanced Lévy driven Ornstein-Uhlenbeck process as a moving average process of the form $X_t=\int \exp(-λ|t-u|)dL_u$. 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 $λ|u|\exp(-λ|u|)$. Furthermore, depending on the size of $λ$ 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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