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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2001-15
June 2001

Normal modified stable processes


Ole E. Barndorff-Nielsen

Neil Shephard


This paper discusses two classes of distributions, and stochastic processes derived from them: modified stable (MS) laws and normal modified stable (NMS) laws. This extends corresponding results for the generalised inverse Gaussian (NGIG) laws. The wider framework thus established provides, in particular, for added flexibility in the modelling of the dynamics of financial time series, of importance especially as regards OU based stochastic volatility models for equities. In the special case of the tempered stable OU process an exact option pricing formula can be found, extending previous results based on the inverse Gaussian and gamma distributions.

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This paper has now been published in Theory Prob. Math. Statist. 65 (2001), 1-19