Hofmann, Bernd ; Krämer, Romy : On maximum entropy regularization for a specific inverse problem of option pricing

Author(s):

Hofmann, Bernd
Krämer, Romy

Title:

On maximum entropy regularization for a specific inverse problem of option pricing

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 6, 2003

Mathematics Subject Classification:

65J20			[ Improperly posed problems; regularization ]
47H30			[ Particular nonlinear operators ]
65R30			[ Improperly posed problems ]
47B07			[ Operators defined by compactness properties ]
91B28			[ Finance, portfolios, investment ]

Abstract:

For a specific inverse problem in option pricing, which is focused on time-dependent functions of volatility and option price data, we investigate the applicability of the method of maximum entropy regularization including convergence and convergence rates of regularized solutions. Due to the explicit structure of the forward operator based on a generalized Black-Scholes formula the ill-posedness character of the nonlinear identification problem under consideration can be verified in detail. Numerical case studies illustrate the chances and limitations of the maximum entropy approach versus Tikhonov regularization for the specific problem.

Keywords:

maximum entropy regularization, nonlinear ill-posed problem, volatility identification, inverse problem, option pricing, convergence rates, numerical case studies

Language:

English

Publication time:

7 / 2003