Abstract
In this paper, we reconstruct the time-dependent volatility function of the underlying asset and the mean-reverting parameter γ of the interest rate for European options under the fractional Chan–Karolyi–Longstaff–Sanders (CKLS) stochastic interest rate model. Tikhonov regularization is used to solve the ill-posedness of the inverse problem. The existence and stability of the solution of the regularization problem are given. We employ the alternating direction method of multipliers (ADMM) to iteratively optimize the volatility function and the parameter γ. Finally, numerical simulations and the empirical analysis are presented to illustrate the efficiency of the proposed method.
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