Before revision:  The classical formula by Dupire, despite being heavily used by industry practitioners , can potentially produce unstable or even singular volatility surfaces ] . In this paper, we propose a new local volatility calibration technique using the theory of optimal transport.
After revision:  The most common approach among industry practitioners is based on the celebrated Dupire's formula ] . In this paper, we propose a new local volatility calibration technique using the theory of optimal transport.