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Calibrating a Diffusion Pricing Model with Uncertain Volatility: Regularization and Stability[Note 1. I would like to thank Marco Avellaneda for introducing ...]
Author(s) -
SAMPERI DOMINICK
Publication year - 2002
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.00005
Subject(s) - regularization (linguistics) , robustness (evolution) , credibility , volatility (finance) , mathematics , stability (learning theory) , sabr volatility model , econometrics , valuation of options , banach space , stochastic volatility , mathematical economics , economics , mathematical optimization , computer science , mathematical analysis , biochemistry , chemistry , artificial intelligence , machine learning , political science , law , gene
A regularized (smoothed) version of the model calibration method of Avellaneda, Friedman, Holmes, and Samperi (1997) is studied. We prove that the regularized formulation is solvable and that the solution depends continuously on the input data (observed derivative security prices). Associated issues of model credibility, stability, and robustness (insensitivity to model assumptions) are discussed. The Implicit Function Theorem for Banach spaces is used for the stability proof, and some numerical illustrations are included.