Well-balanced Lévy driven Ornstein-Uhlenbeck processes
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Date
2010-12-01
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Abstract
In this paper we introduce the well-balanced Lévy driven Ornstein-Uhlenbeck process as a moving average process of the form X_t=integral(exp(-lambda*|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
more slowly. Furthermore, depending on the size of lambda it allows both for positive
and negative correlation of increments. As Ornstein-Uhlenbeck processes X_t is a
stationary process starting at X_0=integral(exp(-lambda*u)dL_u). However, by taking a difference
kernel we can construct a process with stationary increments starting at zero,
which possesses the same correlation structure.
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Keywords
Autocorrelation, Financial modelling, Infinitely divisible distribution, Lèvy process, Ornstein-Uhlenbeck process, Semimartingal