## The normal inverse Gaussian Lévy process: Simulation and approximation.(English)Zbl 0899.60036

Summary: The one- and two-dimensional normal inverse Gaussian Lévy process is studied in relation to German and Danish financial data. In order to investigate if the normal inverse Gaussian Lévy process is a suitable model we calculate the uniform residuals by means of an algorithm which simulates random variables from the normal inverse Gaussian distribution. The algorithm uses the characterization of the normal inverse Gaussian distribution as a normal variance-mean mixture. Finally, an approximation of the process which will make it more tractable from a mathematical finance point of view is provided. Our approximation only relies on the fact that the process is a Lévy process with characteristic triplet $$(\gamma,\sigma^2, \nu)$$ and therefore the method is general and can be applied to any Lévy process.

### MSC:

 60G15 Gaussian processes 60J99 Markov processes 91B28 Finance etc. (MSC2000)
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