宁夏大学学报（自然科学版）2025，Vol.46Issue(1)：24-33,10.
分数阶Black-Scholes模型下的波动率校准问题
Volatility Calibration Problems in A Fractional Black-Scholes Models
摘要
Abstract
In this paper,an accurate and robust numerical algorithm is proposed to invert the volatility function in the fractional Black-Scholes model.First,for the direct problem,considering that the singularity of the pay-off function affects the convergence speed of the L1 method,a finite difference method based on the improved L1 method is proposed.This numerical method can effectively recover the convergence of the L1 method,and only sparse tridiagonal linear systems need to be solved during the computation.Moreover,for the inverse prob-lem,considering the time-dependent volatility function,the volatility inversion problem can be formulated as minimizing the loss function.A continuous and piecewise linear volatility function is constructed and a predictor-corrector approach to mitigate potential oscillations is employed.The results of numerical simulations and empirical analyses demonstrate the accuracy and reliability of the proposed method.关键词
分数阶BS模型/反问题/改进 L1格式/欧式期权/波动率校准Key words
fractional Black-Scholes model/inverse problem/improved L1 method/European options/volatil-ity calibration分类
数学引用本文复制引用
杨培,许作良..分数阶Black-Scholes模型下的波动率校准问题[J].宁夏大学学报（自然科学版）,2025,46(1):24-33,10.基金项目
国家自然科学基金资助项目(12071479) （12071479）
