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 σ(t) of the underlying asset and the fractional order α 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 α and the volatility function σ(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.