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February 2016 Approximating Lévy processes with completely monotone jumps
Daniel Hackmann, Alexey Kuznetsov
Ann. Appl. Probab. 26(1): 328-359 (February 2016). DOI: 10.1214/14-AAP1093

Abstract

Lévy processes with completely monotone jumps appear frequently in various applications of probability. For example, all popular stock price models based on Lévy processes (such as the Variance Gamma, CGMY/KoBoL and Normal Inverse Gaussian) belong to this class. In this paper we continue the work started in [Int. J. Theor. Appl. Finance 13 (2010) 63–91, Quant. Finance 10 (2010) 629–644] and develop a simple yet very efficient method for approximating processes with completely monotone jumps by processes with hyperexponential jumps, the latter being the most convenient class for performing numerical computations. Our approach is based on connecting Lévy processes with completely monotone jumps with several areas of classical analysis, including Padé approximations, Gaussian quadrature and orthogonal polynomials.

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Daniel Hackmann. Alexey Kuznetsov. "Approximating Lévy processes with completely monotone jumps." Ann. Appl. Probab. 26 (1) 328 - 359, February 2016. https://doi.org/10.1214/14-AAP1093

Information

Received: 1 April 2014; Revised: 1 December 2014; Published: February 2016
First available in Project Euclid: 5 January 2016

zbMATH: 1339.60050
MathSciNet: MR3449320
Digital Object Identifier: 10.1214/14-AAP1093

Subjects:
Primary: 60G51
Secondary: 26C15

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.26 • No. 1 • February 2016
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