Finance and Stochastics

, Volume 10, Issue 4, pp 449–474 | Cite as

Spectral calibration of exponential Lévy models



We investigate the problem of calibrating an exponential Lévy model based on market prices of vanilla options. We show that this inverse problem is in general severely ill-posed and we derive exact minimax rates of convergence. The estimation procedure we propose is based on the explicit inversion of the option price formula in the spectral domain and a cut-off scheme for high frequencies as regularisation.


European option Jump diffusion Minimax rates Severely ill-posed Nonlinear inverse problem Spectral cut-off 

Mathematics Subject Classification (2000)

60G51 62G20 91B28 

JEL Classification

G13 C14 


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Weierstraß Institute for Applied Analysis and Stochastics (WIAS)BerlinGermany
  2. 2.Institute of Applied MathematicsUniversity of HeidelbergHeidelbergGermany

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