Maximum entropy regularization for calibrating a time-dependent volatility function

• Main Authors: Hofmann, Bernd, Krämer, Romy
• Other Authors: TU Chemnitz, Fakultät für Mathematik
• Format: Others
• Language: English
• Published: Universitätsbibliothek Chemnitz 2004
• Subjects: Tikhonov regularization; convergence rate; inverse problem; maximum entropy regularization; volatility calibration; ddc:510
• Online Access: http://nbn-resolving.de/urn:nbn:de:swb:ch1-200401213; http://nbn-resolving.de/urn:nbn:de:swb:ch1-200401213; http://www.qucosa.de/fileadmin/data/qucosa/documents/4869/data/ho_kr_tagungsband_2003.pdf; http://www.qucosa.de/fileadmin/data/qucosa/documents/4869/20040121.txt

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.