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Sensitivity Analysis for Time-Inhomogeneous Lévy Process: A Malliavin Calculus Approach and Numerics

  • M’hamed EddahbiEmail author
  • Sidi Mohamed Lalaoui Ben Cherif
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 158)

Abstract

The main goal of this paper is to study sensitivity analysis, with respect to the parameters of the model, in the framework of time-inhomogeneous Lévy process. This is a slight generalization of recent results of Fournié et al. (Finance Stochast 3(4):391–412, 1999 [9]), El-Khatib and Privault (Finance Stochast 8(2):161–179, 2004 [7]), Bally et al. (Ann Appl Probab 17(1):33–66, 2007 [1]), Davis and Johansson (Stochast Process Appl 116(1):101–129, 2006 [5]), Petrou (Electron J Probab 13(27):852–879, 2008 [12]), Benth et al. (Commun Stochast Anal 5(2):285–307, 2011 [2]) and El-Khatib and Hatemi (J Statist Appl Probab 3(1):171–182, 2012 [8]), using Malliavin calculus developed by Yablonski (Rocky Mountain J Math 38:669–701, 2008 [16]). This relatively recent result will help us to provide tools that are necessary for the calculation of the sensitivities. We provide some simple examples to illustrate the results achieved. In particular, we discussed the time-inhomogeneous versions of the Merton model and the Bates model.

Keywords

Additive processes Time-inhomogeneous lévy process Malliavin calculus Integration by parts formula Sensitivity analysis 

Mathematics Subject Classification 2010

60H07 60H35 60G51 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • M’hamed Eddahbi
    • 1
    Email author
  • Sidi Mohamed Lalaoui Ben Cherif
    • 1
    • 2
  1. 1.Faculty of Sciences and Techniques, Department of MathematicsCadi Ayyad UniversityMarrakechMorocco
  2. 2.Faculty of Sciences Semlalia, Department of MathematicsCadi Ayyad UniversityMarrakeshMorocco

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