The calibration of volatility for European option under fractional stochastic interest rate model
Year: 2025
Type: article
Abstract: 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.
DOI: 10.3934/jimo.2025057
Authors: Jiajia Zhao, Zuoliang Xu
Institution: Renmin University of China
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: diamond
OpenAlex ID: W4408992917