Convergence rates results for recovering the volatility term structure including at-the-money options

DOI10.1515/JIIP.2009.024zbMath1177.35251MaRDI QIDQ5191062

Torsten Hein

Publication date: 28 July 2009

Published in: Journal of Inverse and Ill-posed Problems (Search for Journal in Brave)

zbMATH Keywords

regularizationBlack-Scholes modelparabolic equationsill-posed probleminverse problem of option pricingidentification of local volatilities

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Positional games (pursuit and evasion, etc.) (91A24)

Cites Work

• The Pricing of Options and Corporate Liabilities
• Identifying the volatility of underlying assets from option prices
• Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
• Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets
• Factors influencing the ill-posedness of nonlinear problems
• 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
• Convergence rates of convex variational regularization
• 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