On Tikhonov regularization method in calibration of volatility term-structure

Authors

Ahmad Reza Yazdanian, Iran University of Science and TechnologyFollow

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.

Recommended Citation

Reza Yazdanian, Ahmad (2013) "On Tikhonov regularization method in calibration of volatility term-structure," Information Sciences Letters: Vol. 2 : Iss. 2 , PP -.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol2/iss2/7