WIAS Preprint No. 1017, (2005)

Optimal calibration for exponential Levy models



Authors

  • Belomestny, Denis
  • Reiss, Markus

2010 Mathematics Subject Classification

  • 62G20 60G51 91B28

Keywords

  • European option, jump diffusion, minimax rates, severely ill-posed, nonlinear inverse problem, spectral cut-off

Abstract

Based on options data at the market the problem of calibrating an exponential Lévy model for the underlying asset is investigated. It is shown that this statistical inverse problem is in general severely ill-posed and exact minimax rates of convergence are derived. 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. Its performance is illustrated by numerical simulations.

Appeared in

  • Finance Stoch., 10 (2006) pp. 449--474.

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