Spectral calibration of exponential Lévy Models 
AbstractThe 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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Bibliographic InfoPaper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-035.
Length: 20 pages
Date of creation: Apr 2006
Date of revision:
European option; jump diffusion; minimax rates; severely ill-posed; nonlinear inverse problem; spectral cut-off;
Other versions of this item:
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-05-13 (All new papers)
- NEP-ECM-2006-05-13 (Econometrics)
- NEP-FIN-2006-05-13 (Finance)
- NEP-FMK-2006-05-13 (Financial Markets)
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