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Sensitivities and Greeks

  • Norbert Hilber
  • Oleg Reichmann
  • Christoph Schwab
  • Christoph Winter
Part of the Springer Finance book series (FINANCE)

Abstract

A key task in financial engineering is the fast and accurate calculation of sensitivities of market models with respect to model parameters. This becomes necessary, for example, in model calibration, risk analysis and in the pricing and hedging of certain derivative contracts. Classical examples are variations of option prices with respect to the spot price or with respect to time-to-maturity, the so-called “Greeks” of the model. For classical, diffusion type models and plain vanilla type contracts, the Greeks can be obtained analytically. With the trends to more general market models of jump–diffusion type and to more complicated contracts, closed form solutions are generally not available for pricing and calibration. Thus, prices and model sensitivities have to be approximated numerically.

Keywords

Option Price Market Model Dirichlet Form Separable Hilbert Space Infinitesimal Generator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Y. Achdou and O. Pironneau. Computational methods for option pricing, volume 30 of Frontiers in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2005. zbMATHCrossRefGoogle Scholar
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    N. Hilber, Ch. Schwab, and Ch. Winter. Variational sensitivity analysis of parametric Markovian market models. In Ł. Stettner, editor, Advances in mathematics of finance, volume 83, of Banach Center Publ., pages 85–106. 2008. CrossRefGoogle Scholar
  3. 140.
    O. Reiss and U. Wystup. Efficient computation of option price sensitivities using homogeneity and other tricks. J. Deriv., 9:41–53, 2001. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Norbert Hilber
    • 1
  • Oleg Reichmann
    • 2
  • Christoph Schwab
    • 2
  • Christoph Winter
    • 3
  1. 1.Dept. for Banking, Finance, Insurance, School of Management and LawZurich University of Applied SciencesWinterthurSwitzerland
  2. 2.Seminar for Applied MathematicsSwiss Federal Institute of Technology (ETH)ZurichSwitzerland
  3. 3.Allianz Deutschland AGMunichGermany

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