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Measure Changes in Finance

Author

Listed:
  • Olivier Le Courtois

    (EM - EMLyon Business School)

  • François Quittard-Pinon

Abstract

Changes of measure are known in standard finance, but when modelling assets with Lévy processes these changes become something more refined. In particular, the use of Lévy processes does not permit building of a complete market. In other words, the risk-neutral measure is not unique; prices will vary according to the choice of measure that is made. Two approaches are basically available. In the first approach (cf. Carr, Geman, Madan and Yor (2002)), the risk-neutral measure is extracted directly from the market -- from option prices. One can then compute derivative prices by performing numerical integrations with respect to this measure. In the second approach (cf. Raible (2000)), the risk-neutral measure is derived by an Esscher transform. Users of this approach (Raible and others) modelled prices on processes from the Generalized Hyperbolic class.

Suggested Citation

  • Olivier Le Courtois & François Quittard-Pinon, 2004. "Measure Changes in Finance," Post-Print hal-02312484, HAL.
    • Handle: RePEc:hal:journl:hal-02312484
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