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Information Sciences Letters

Information Sciences Letters

Abstract

In this paper, we consider inverse problem arising in calibration of time-dependent volatility function from the Black-Scholes model and analyze its ill-posedness phenomena. The forward operator of the inverse problem under some consideration decomposes into an inner linear convolution operator and an outer nonlinear Nemytskii operator given by a Black-Scholes function. Using Chebyshev collocation method, we transfer the inner linear operator to a linear system. Since the resulting matrix equation is badly ill-conditioned, a regularized solution is obtained by employing the Tikhonov regularization method, while the choice of the regularization parameter are based on generalized cross-validation(GCV) and L-curve criterions. Numerical case studies illustrate the effciency and accuracy of the presented method.

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