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We explore the abilities of two machine learning approaches for no-arbitrageinterpolation of European vanilla option prices, which jointly yield thecorresponding local volatility surface: a finite dimensional Gaussian process(GP) regression approach under no-arbitrage constraints based on prices, and aneural net (NN) approach with penalization of arbitrages based on impliedvolatilities. We demonstrate the performance of these approaches relative tothe SSVI industry standard. The GP approach is proven arbitrage-free, whereasarbitrages are only penalized under the SSVI and NN approaches. The GP approachobtains the best out-of-sample calibration error and provides uncertaintyquantification.The NN approach yields a smoother local volatility and a betterbacktesting performance, as its training criterion incorporates a localvolatility regularization term.

Beyond Surrogate Modeling: Learning the Local Volatility Via Shape Constraints