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