Measure Changes in Finance

in Finance India, 18(1)

ISSN : 0970-3772

Le Courtois, Olivier (1975-....) ; Quittard-Pinon, François (1945-....)

Voir la revue «Finance India»

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.

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