Ill-posedness versus ill-conditioning–an example from inverse option pricing

DOI10.1080/00036810802032136zbMath1152.91527OpenAlexW2010103157MaRDI QIDQ3497834

Romy Krämer, Matthias Richter

Publication date: 28 May 2008

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036810802032136

zbMATH Keywords

regularizationNemytskii operatorvolatility calibrationinverse problem of option pricing

Mathematics Subject Classification ID

Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Derivative securities (option pricing, hedging, etc.) (91G20) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (4)

Calibration of the purely T-dependent Black–Scholes implied volatility ⋮ Recovery of the local volatility function using regularization and a gradient projection method ⋮ Some aspects of parameter identification in a mean reverting financial asset model with time-dependent volatility ⋮ Simultaneous identification of volatility and interest rate functions -- a two-parameter regularization approach

Cites Work

• Identifying the volatility of underlying assets from option prices
• Retrieving Lévy Processes from Option Prices: Regularization of an Ill-posed Inverse Problem
• Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets
• The inverse problem of option pricing
• Calibration of the Local Volatility in a Generalized Black--Scholes Model Using Tikhonov Regularization
• On the nature of ill-posedness of an inverse problem arising in option pricing
• Calibrating volatility surfaces via relative-entropy minimization
• COMPUTATION OF LOCAL VOLATILITIES FROM REGULARIZED DUPIRE EQUATIONS
• A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators
• Tikhonov regularization applied to the inverse problem of option pricing: convergence analysis and rates
• On decoupling of volatility smile and term structure in inverse option pricing

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