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

Abstract

We investigate the applicability of the method of maximum entropy regularization (MER) to a specific nonlinear ill-posed inverse problem (SIP) in a purely time-dependent model of option pricing, introduced and analyzed for an L2 -setting in [9]. In order to include the identification of volatility functions with a weak pole, we extend the results of [12, 13], concerning convergence and convergence rates of regularized solutions in L1 , in some details. Numerical case studies illustrate the chances and limitations of (MER) versus Tikhonov regularization (TR) for smooth solutions and solutions with a sharp peak. A particular paragraph is devoted to the singular case of at-the-money options, where derivatives of the forward operator degenerate.