Calibration of the purely T-dependent Black–Scholes implied volatility

Abstract

We consider the problem of recovering an implied volatility from the data of option price. We improve results of Hein and Hofmann, and Kramer and Richter. In fact, we shall construct an elementary regularization. Then, we give an explicit formula of the regularization parameter. An explicit error estimate is also given.

Keywords:

• calibration
• volatility
• ill-posed
• regularization

AMS Subject Classifications:

• 35R30
• 65J20
• 91B24

Acknowledgments

The authors would like to thank the referees for the kind and deep opinions leading to the improvement version of our paper. This paper is supported by NAFOSTED (Project 101.01-2012.07).