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Spectral calibration of exponential Lévy Models [2]

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Author Info
Denis Belomestny
Markus Reiß

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Abstract

The calibration of financial models has become rather important topic in recent years mainly because of the need to price increasingly complex options in a consistent way. The choice of the underlying model is crucial for the good performance of any calibration procedure. Recent empirical evidences suggest that more complex models taking into account such phenomenons as jumps in the stock prices, smiles in implied volatilities and so on should be considered. Among most popular such models are Levy ones which are on the one hand able to produce complex behavior of the stock time series including jumps, heavy tails and on other hand remain tractable with respect to option pricing. The work on calibration methods for financial models based on Lévy processes has mainly focused on certain parametrisations of the underlying Lévy process with the notable exception of Cont and Tankov (2004). Since the characteristic triplet of a Lévy process is a priori an infinite-dimensional object, the parametric approach is always exposed to the problem of misspecification, in particular when there is no inherent economic foundation of the parameters and they are only used to generate different shapes of possible jump distributions. In this work we propose and test a non-parametric calibration algorithm which is based on the inversion of the explicit pricing formula via Fourier transforms and a regularisation in the spectral domain. Using the Fast Fourier Transformation, the procedure is fast, easy to implement and yields good results in simulations in view of the severe ill-posedness of the underlying inverse problem.

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Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-035.

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Length: 20 pages
Date of creation: Apr 2006
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Handle: RePEc:hum:wpaper:sfb649dp2006-035

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Related research
Keywords: European option; jump diffusion; minimax rates; severely ill-posed; nonlinear inverse problem; spectral cut-off;

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Find related papers by JEL classification:
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Bruno Deffains & Dominique Demougin, 2006. "Institutional Competition, Political Process and Holdup," SFB 649 Discussion Papers SFB649DP2006-027, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  2. Benjamin Bental & Dominique Demougin, 2006. "Institutions, Bargaining Power and Labor Shares," SFB 649 Discussion Papers SFB649DP2006-009, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  3. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy Models [1]," SFB 649 Discussion Papers SFB649DP2006-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
    Other versions:
  4. Yasemin Boztug & Thomas Reutterer, 2006. "A Combined Approach for Segment-Specific Analysis of Market Basket Data," SFB 649 Discussion Papers SFB649DP2006-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  5. Trabandt, Mathias & Uhlig, Harald, 2006. "How Far Are We From the Slippery Slope? The Laffer Curve Revisited," CEPR Discussion Papers 5657, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  6. Daniel Hernandez–Hernandez & Alexander Schied, 2005. "Robust Utility Maximization in a Stochastic Factor Model," SFB 649 Discussion Papers SFB649DP2006-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Aug 2006. [Downloadable!]
  7. Michel A. Robe & Eva-Maria Steiger & Pierre-Armand Michel, 2006. "Penalties and Optimality in Financial Contracts: Taking Stock," SFB 649 Discussion Papers SFB649DP2006-013, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  8. Lydia Mechtenberg & Roland Strausz, . "The Bologna Process: How student mobility affects multi-cultural skills and educational quality," Papers 030, Departmental Working Papers. [Downloadable!]
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  9. Enzo Weber, 2006. "British Interest Rate Convergence Between The Us And Europe: A Recursive Cointegration Analysis," Icfai University Journal of Monetary Economics, Icfai Press, vol. 0(4), pages 29-47, November.
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  10. Dominique Demougin & Anja Schöttner, 2006. "Technological Choice under Organizational Diseconomies of Scale," SFB 649 Discussion Papers SFB649DP2006-028, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  11. Kurt Geppert & Martin Gornig & Axel Werwatz, 2006. "Economic Growth of Agglomerations and Geographic Concentration of Industries – Evidence for Germany," SFB 649 Discussion Papers SFB649DP2006-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  12. Carsten Trenkler, 2006. "Bootstrapping Systems Cointegration Tests with a Prior Adjustment for Deterministic Terms," SFB 649 Discussion Papers SFB649DP2006-012, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  13. Harald Uhlig, 2006. "Approximate Solutions to Dynamic Models - Linear Methods," SFB 649 Discussion Papers SFB649DP2006-030, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  14. Harald Uhlig, 2006. "Regional Labor Markets, Network Externalities and Migration: The Case of German Reunification," American Economic Review, American Economic Association, vol. 96(2), pages 383-387, May. [Downloadable!]
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  15. Wolfgang Härdle & Sigbert Klinke & Uwe Ziegenhagen, 2006. "e-Learning Statistics - A Selective Review," SFB 649 Discussion Papers SFB649DP2006-024, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  16. Enzo Giacomini & Michael Handel & Wolfgang K. Härdle, 2006. "Time Dependent Relative Risk Aversion," SFB 649 Discussion Papers SFB649DP2006-020, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  17. Andreas Thams, 2006. "Fiscal Policy Effects in the European Union," SFB 649 Discussion Papers SFB649DP2006-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  18. Ralf Brüggemann & Wolfgang Härdle & Julius Mungo & Carsten Trenkler, 2006. "VAR Modeling for Dynamic Semiparametric Factors of Volatility Strings," SFB 649 Discussion Papers SFB649DP2006-011, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Christian Stoltenberg, 2006. "Real Balance Effects, Timing and Equilibrium Determination," SFB 649 Discussion Papers SFB649DP2006-073, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  2. Bruno Deffains & Dominique Demougin, 2006. "Governance: Who Controls Matters," SFB 649 Discussion Papers SFB649DP2006-053, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  3. Dirk Temme & Henning Kreis & Lutz Hildebrandt, 2006. "PLS Path Modeling – A Software Review," SFB 649 Discussion Papers SFB649DP2006-084, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  4. Matthias Paustian & Christian Stoltenberg, 2006. "Optimal Interest Rate Stabilization in a Basic Sticky-Price Model," SFB 649 Discussion Papers SFB649DP2006-072, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  5. Zdenek Hlavka & Michal Pesta, 2006. "Constrained General Regression in Pseudo-Sobolev Spaces with Application to Option Pricing," SFB 649 Discussion Papers SFB649DP2006-069, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  6. Szymon Borak & Wolfgang Härdle & Stefan Trück & Rafal Weron, 2006. "Convenience Yields for CO2 Emission Allowance Futures Contracts," SFB 649 Discussion Papers SFB649DP2006-076, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  7. Jenny Kragl & Julia Schmid, 2006. "Relational Contracts and Inequity Aversion," SFB 649 Discussion Papers SFB649DP2006-085, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  8. Taleb Ahmad & Wolfgang Härdle & Julius Mungo, 2006. "On the Difficulty to Design Arabic E-learning System in Statistics," SFB 649 Discussion Papers SFB649DP2006-062, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  9. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy Models [2]," SFB 649 Discussion Papers SFB649DP2006-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
    Other versions:
  10. Kai Detlefsen & Wolfgang Härdle, 2006. "Forecasting the Term Structure of Variance Swaps," SFB 649 Discussion Papers SFB649DP2006-052, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  11. Tim Grebe & Julia Schmid & Andreas Stiehler, 2006. "Do Individuals Recognize Cascade Behavior of Others? - An Experimental Study -," SFB 649 Discussion Papers SFB649DP2006-079, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  12. Dirk Temme & Lutz Hildebrandt, 2006. "Formative Measurement Models in Covariance Structure Analysis: Specification and Identification," SFB 649 Discussion Papers SFB649DP2006-083, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  13. Enzo Giacomini & Wolfgang Härdle & Ekaterina Ignatieva & Vladimir Spokoiny, 2006. "Inhomogeneous Dependency Modelling with Time Varying Copulae," SFB 649 Discussion Papers SFB649DP2006-075, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  14. Ying Chen & Wolfgang Härdle & Vladimir Spokoiny, 2006. "GHICA - Risk Analysis with GH Distributions and Independent Components," SFB 649 Discussion Papers SFB649DP2006-078, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  15. Carsten Trenkler & Pentti Saikkonen & Helmut Lütkepohl, 2006. "Testing for the Cointegrating Rank of a VAR Process with Level Shift and Trend Break," SFB 649 Discussion Papers SFB649DP2006-067, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  16. Dominique Demougin & Oliver Fabel, 2006. "The Division of Ownership in New Ventures," SFB 649 Discussion Papers SFB649DP2006-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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