ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis ISBN 978-3-7001-8258-0 Online Edition Research Article
Christopher Hofmann,
Bernd Hofmann,
Alois Pichler
S. 99 - 117 doi:10.1553/etna_vol51s99 Verlag der Österreichischen Akademie der Wissenschaften doi:10.1553/etna_vol51s99
Abstract: This paper investigates a specific ill-posed nonlinear inverse problem that arises in financial markets. Precisely, as a benchmark problem in the context of volatility surface calibration, we consider the simultaneous recovery of implied volatility and interest rate functions over a finite time interval from corresponding call- and put-price functions for idealized continuous families of European vanilla options over the same maturity interval. We prove identifiability of the pair of functions to be identified by showing injectivity of the forward operator in L2-spaces. To overcome the ill-posedness we employ a two-parameter Tikhonov regularization with heuristic parameter choice rules and demonstrate chances and limitations by means of numerical case studies using synthetic data. Keywords: inverse option pricing, simultaneous identification, volatility, interest rate, regularization Published Online: 2019/04/15 10:02:24 Object Identifier: 0xc1aa5576 0x003a98c8 Rights: . Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613. …
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |