Simulation of Student–Lévy processes using series representations

Till Massing ()
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Till Massing: University of Duisburg-Essen

Computational Statistics, 2018, vol. 33, issue 4, No 5, 1649-1685

Abstract: Abstract Lévy processes have become very popular in many applications in finance, physics and beyond. The Student–Lévy process is one interesting special case where increments are heavy-tailed and, for 1-increments, Student t distributed. Although theoretically available, there is a lack of path simulation techniques in the literature due to its complicated form. In this paper we address this issue using series representations with the inverse Lévy measure method and the rejection method and prove upper bounds for the mean squared approximation error. In the numerical section we discuss a numerical inversion scheme to find the inverse Lévy measure efficiently. We extend the existing numerical inverse Lévy measure method to incorporate explosive Lévy tail measures. Monte Carlo studies verify the error bounds and the effectiveness of the simulation routine. As a side result we obtain series representations of the so called inverse gamma subordinator which are used to generate paths in this model.

Keywords: Lévy process; Student t distribution; Sample path simulation; Pure jump process; Numerical inversion; Simulation study (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00180-018-0814-y

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