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 classical formula by Dupire, despite being heavily used by industry practitioners , can potentially produce unstable or even singular volatility surfaces ], which requires the knowledge of vanilla option prices for a continuum of strikes and maturities that can only be obtained via some form of price interpolation . In this paper, we propose a new local volatility calibration technique using the theory of optimal transport.