We investigate the applicability of the method of maximum entropy regularization (MER) including convergence and convergence rates of regularized solutions to
the specific inverse problem (SIP) of calibrating a purely time-dependent volatility
function. In this context, we extend the results of [16] and [17] in some details.
Due to the explicit structure of the forward operator based on a generalized Black-Scholes formula the ill-posedness character of the nonlinear inverse problem (SIP)
can be verified. Numerical case studies illustrate the chances and limitations of
(MER) versus Tikhonov regularization (TR) for smooth solutions and solutions
with a sharp peak.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:swb:ch1-200401213 |
| Date | 26 August 2004 |
| Creators | Hofmann, Bernd, Krämer, Romy |
| Contributors | TU Chemnitz, Fakultät für Mathematik |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:lecture |
| Format | application/pdf, text/plain, application/zip |
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