A New Regularized Algorithm to Calibrate Implied Volatility in Option Pricing Models

This paper discusses the problem of calibrating volatility from a finite set of observed option prices. This kind of inverse problems, where one looks for causes of observed effects, are usually ill-posed. We propose a regularized Gauss-Newton method to calibrate the implied volatility in a stable way. Bakushinskii iterative algorithm is developed for solving the regularization problem. Finally, the theoretical results are illustrated by numerical experiment.