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عمومی::
فرآیند لوی پرش محض
Recently, Barndorff-Nielsen and Shephard (2001a, b) sug- gested a completely new class of models, termed non-Gaussian Ornstein-Uhlenbeck (OU) models, in which the driving process for a volatility factor is a pure-jump Lévy process with non- negative increments; simple parametric sign restrictions ensure positivity.
Here we introduce the series representation of pure-jump Lévy processes.
This theorem provides a way to represent pure-jump Lévy processes and integrals with respect to them.
This Lévy process is a superposition of the pure-jump Lévy processes used by Carr, Geman, Madan, and Yor (2002, 2003) with the tilting parameter set to 0.
To accommodate the leverage effect in the stochastic volatil- ity model, we need a two-dimensional pure-jump Lévy process with linked individual processes.
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