The calibration of volatility for option pricing models with jump diffusion processes

作     者：Xu, Zuoliang Jia, Xiangyu 

作者机构：Renmin Univ China Sch Informat Beijing Peoples R China 

出 版 物：《APPLICABLE ANALYSIS》 (适用分析)

年 卷 期：2019年第98卷第4期

页      面：810-827页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：National Natural Science Foundation of China 

主　　题：Jump-diffusion model Tikhonov regularization Euler-Lagrange equation the finite difference method iterative algorithm 

摘      要：This paper is devoted to calibrate smooth local volatility surface under jump-diffusion processes. This calibration problem is posed as an inverse problem: given a finite set of observed European option prices, find a local volatility function such that the theoretical option prices matches the observed ones optimally with respect to a prescribed performance criterion. Firstly, we obtain an Euler-Lagrange equation for the calibration problem using Tikhonov regularization method. Then we solve the Euler-Lagrange equation using an iterative algorithm and obtain the volatility. Finally, numerical experiments show the effectiveness of the proposed method.