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

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.