Calibration of time-dependent volatility for European options under the fractional Vasicek model

In this paper, we calibrate the time-dependent volatility function for European options under the fractional Vasicek interest rate model. A fully implicit finite difference method is applied to solve the partial differential equation of option pricing numerically. To find the volatility function, we minimize a cost function that is the sum of the squared errors between the theoretical prices and market prices with Tikhonov $L_2$ regularization and $L_{1/2}$ regularization respectively. Finally numerical experiments with simulated and real market data verify the efficiency of the proposed methods.