The calibration of volatility for European option under fractional stochastic interest rate model

In this paper, we discuss the calibration of the time-dependent volatility function from European option prices. Firstly, a time-fractional stochastic interest rate model is proposed by combining the fractional-order stochastic differential equation for the underlying asset with the stochastic interest rate process to capture the memory effect in the financial market. Secondly, we employ the modified Landweber iteration to calibrate the volatility from a finite set of discrete market observations. In particular, we prove that the parameter-to-solution map associated to the inverse problem satisfies the local tangential cone condition. The convergence analysis of the regularized solution is presented. Finally, several examples and empirical analysis are given to demonstrate the effectiveness of the proposed method.