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Spectral calibration of exponential Lévy Models [1]

By Denis Belomestny and Markus Reiß

Abstract

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

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  1. (2006). A Combined Approach for Segment-Specific Analysis of Market Basket Data" by Yasemin Boztuğ and Thomas Reutterer,
  2. (2003). A±ne processes and applications in ¯nance.,"
  3. (2006). Approximate Solutions to Dynamic Models – Linear Methods" by Harald Uhlig,
  4. (2006). Barrier Option Hedging under Constraints: A Viscosity Approach" by Imen Bentahar
  5. (2006). Bootstrapping Systems Cointegration Tests with a Prior Adjustment for Deterministic Terms" by Carsten Trenkler,
  6. (2006). British Interest Rate Convergence between the US and Europe: A Recursive Cointegration Analysis" by Enzo Weber,
  7. (2006). Calibration Design of Implied Volatility Surfaces" by Kai Detlefsen
  8. (2006). Calibration Risk for Exotic Options" by Kai Detlefsen
  9. (2006). Cheap Talk in the Classroom" by Lydia Mechtenberg,
  10. (2006). Common Functional Principal Components" by Michal Benko, Wolfgang Härdle and Alois Kneip,
  11. (2006). Core Labour Standards and FDI: Friends or Foes? The Case of Child Labour" by Sebastian Braun,
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  13. (2006). Economic Growth of Agglomerations and Geographic Concentration of Industries - Evidence for Germany" by Kurt Geppert, Martin Gornig and Axel Werwatz,
  14. (2006). Estimation with the Nested Logit Model: Specifications and Software Particularities" by Nadja Silberhorn, Yasemin Boztuğ and Lutz Hildebrandt,
  15. (2006). Exploratory Graphics of a Financial Dataset" by Antony Unwin, Martin Theus and Wolfgang Härdle,
  16. (2006). Finite Sample Properties of Impulse Response Intervals in SVECMs with Long-Run Identifying Restrictions" by Ralf Brüggemann,
  17. (2006). Fiscal Policy Effects in the European Union" by Andreas Thams,
  18. (2006). Graphical Data Representation in Bankruptcy Analysis" by Wolfgang Härdle, Rouslan Moro and Dorothea Schäfer,
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  23. (2003). Nonparametric option pricing under shape restrictions.,"
  24. (2006). On the Appropriateness of Inappropriate VaR Models" by Wolfgang Härdle, Zdeněk Hlávka
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  27. (2006). Regional Labor Markets, Network Externalities and Migration: The Case of German Reunification" by Harald Uhlig,
  28. (2006). Robust utility maximization in a stochastic factor model" by Daniel Hernández–Hernández and Alexander Schied,
  29. (2006). Spectral calibration of exponential Lévy Models [1]" by Denis Belomestny
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  34. (2006). Time Dependent Relative Risk Aversion" by Enzo Giacomini, Michael Handel and Wolfgang Härdle,
  35. (2005). uppelberg (2004): \Optimal portfolios when stock prices follow an exponential L¶ evy process,"
  36. (2006). VAR Modeling for Dynamic Semiparametric Factors of Volatility Strings" by Ralf Brüggemann, Wolfgang Härdle, Julius Mungo and Carsten Trenkler,
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