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

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Statistical Methods and Applications in Insurance and Finance (CIMPA School 2013)

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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.

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Notes

  1. 1.

    This is to ensure that we can find some solutions for the weighting functions, since it often requires to take the inverse of the volatility function.

  2. 2.

    Cox, Ingersoll and Ross model. See [4].

References

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Author information

Authors and Affiliations

  1. Faculty of Sciences and Techniques, Department of Mathematics, Cadi Ayyad University, B.P. 549, Marrakech, Morocco

    M’hamed Eddahbi & Sidi Mohamed Lalaoui Ben Cherif

  2. Faculty of Sciences Semlalia, Department of Mathematics, Cadi Ayyad University, B.P. 2390, Marrakesh, Morocco

    Sidi Mohamed Lalaoui Ben Cherif

Authors
  1. M’hamed Eddahbi
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  2. Sidi Mohamed Lalaoui Ben Cherif
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Correspondence to M’hamed Eddahbi .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Université Cadi Ayyad Department of Mathematics, Marrakesh, Morocco

    M'hamed Eddahbi

  2. Faculté Polydisciplinaire, Université Cadi Ayyad, Safi, Morocco

    El Hassan Essaky

  3. Faculty of Mathematics, University of Barcelona, Barcelona, Spain

    Josep Vives

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Eddahbi, M., Lalaoui Ben Cherif, S.M. (2016). Sensitivity Analysis for Time-Inhomogeneous Lévy Process: A Malliavin Calculus Approach and Numerics. In: Eddahbi, M., Essaky, E., Vives, J. (eds) Statistical Methods and Applications in Insurance and Finance. CIMPA School 2013. Springer Proceedings in Mathematics & Statistics, vol 158. Springer, Cham. https://doi.org/10.1007/978-3-319-30417-5_2

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