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

ABSTRACT

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.

KEYWORDS:

• Jump-diffusion model
• Tikhonov regularization
• Euler–Lagrange equation
• the finite difference method
• iterative algorithm

AMS SUBJECT CLASSIFICATIONS:

• 60J75
• 65C20
• 91B28

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by National Natural Science Foundation of China [grant number 11571365].