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Efficient calculation of the Greeks for exponential Lévy processes: an application of measure valued differentiation

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  • Georg Ch. Pflug
  • Philipp Thoma

Abstract

Monte Carlo simulation methods have become more and more important in the financial sector in the past years. In this paper, we introduce a new simulation method for the estimation of the derivatives of prices of financial contracts with respect to (w.r.t.) certain distributional parameters called the ‘Greeks’. In particular, we assume that the underlying financial process is a Lévy-type process in discrete time. Our method is based on the Measure-Valued Differentiation (MVD) approach, which allows representation of derivatives as differences of two processes, called the phantoms. We discuss the applicability of MVD for different types of option pay-offs in combination with different types of models of the underlying and provide a framework for the applicability of MVD for path-dependent pay-off functions, as Lookback Options or Asian Options.

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  • Georg Ch. Pflug & Philipp Thoma, 2016. "Efficient calculation of the Greeks for exponential Lévy processes: an application of measure valued differentiation," Quantitative Finance, Taylor & Francis Journals, vol. 16(2), pages 247-257, February.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:2:p:247-257
    DOI: 10.1080/14697688.2015.1114364
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    1. Montero, Miquel & Kohatsu-Higa, Arturo, 2003. "Malliavin Calculus applied to finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 548-570.
    2. Heidergott, Bernd & Vazquez-Abad, Felisa J. & Volk-Makarewicz, Warren, 2008. "Sensitivity estimation for Gaussian systems," European Journal of Operational Research, Elsevier, vol. 187(1), pages 193-207, May.
    3. Bernd Heidergott & Haralambie Leahu, 2010. "Weak Differentiability of Product Measures," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 27-51, February.
    4. Peter W. Glynn & Ward Whitt, 1992. "The Asymptotic Efficiency of Simulation Estimators," Operations Research, INFORMS, vol. 40(3), pages 505-520, June.
    5. Arturo Kohatsu & Montero Miquel, 2003. "Malliavin calculus in finance," Economics Working Papers 672, Department of Economics and Business, Universitat Pompeu Fabra.
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    Cited by:

    1. Anselm Hudde & Ludger Rüschendorf, 2023. "European and Asian Greeks for Exponential Lévy Processes," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-24, March.

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