Normal Modified Stable Processes

Neil Shephard · Ole Eiler Barndorff-Nielsen

128 citations0/0 files storedOxford University Research Archive (ORA) (University of Oxford)

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Stochastic processes and financial applications Probability and Statistical Research Probability and Risk Models

Abstract

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 (GIG) and generalised hyperbolic (GH) or normal 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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References

1987The Pricing of Options on Assets with Stochastic Volatilities 2000An Introduction to Econophysics: Correlations and Complexity in Finance 2002Econometric Analysis of Realized Volatility and its Use in Estimating Stochastic Volatility Models 1998The Variance Gamma Process and Option Pricing 2002The Fine Structure of Asset Returns: An Empirical Investigation 1997Processes of normal inverse Gaussian type 19965 Stochastic volatility 1997Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling

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