Simultaneous Calibration of European Option Volatility and Fractional Order under the Time Fractional Vasicek Model

In this paper, we recover the European option volatility function sigma(t) of the underlying asset and the fractional order alpha of the time fractional derivatives under the time fractional Vasicek model. To address the ill-posed nature of the inverse problem, we employ Tikhonov regularization. The Alternating Direction Multiplier Method (ADMM) is utilized for the simultaneous recovery of the parameter alpha and the volatility function sigma(t). In addition, the existence of a solution to the minimization problem has been demonstrated. Finally, the effectiveness of the proposed approach is verified through numerical simulation and empirical analysis.