Spectral calibration of exponential Lévy models

DOI10.1007/s00780-006-0021-5zbMath1126.91022OpenAlexW2167569669MaRDI QIDQ881412

Denis Belomestny, Markus Reiss

Publication date: 29 May 2007

Published in: Finance and Stochastics (Search for Journal in Brave)

Full work available at URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-034.pdf

zbMATH Keywords

European optionjump diffusionminimax ratesnonlinear inverse problemseverely ill-posedspectral cut-off

Mathematics Subject Classification ID

Related Items (46)

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Cites Work

• A Jump-Diffusion Model for Option Pricing
• Minimax theory of image reconstruction
• Spectral calibration of exponential Lévy models
• Volatility estimators for discretely sampled Lévy processes
• Asymptotic equivalence of nonparametric regression and white noise
• Nonparametric option pricing under shape restrictions
• Optimal portfolios for exponential Lévy processes.
• Optimal stopping and perpetual options for Lévy processes
• Affine processes and applications in finance
• Minimax estimation of the noise level and of the deconvolution density in a semiparametric convolution model
• Optimal portfolios when stock prices follow an exponential Lévy process
• Integro-differential equations for option prices in exponential Lévy models
• Optimal change-point estimation from indirect observations
• Semiparametric modeling of implied volatility.
• Retrieving Lévy Processes from Option Prices: Regularization of an Ill-posed Inverse Problem
• Calibration of the Local Volatility in a Generalized Black--Scholes Model Using Tikhonov Regularization
• Financial Modelling with Jump Processes
• Option pricing when underlying stock returns are discontinuous

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