Arbitrage-free smoothing of the implied volatility surface

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Common functional principal components (2009, unknown): “For comprehensive monographs on IV and IV-factor models, see Hafner (2004) or Fengler (2005b). The idea of constructing and analyzing the factor models for log-IVreturns for different maturities was originally proposed by Fengler, Härdle and Villa (2003), who studied the dynamics of the IV via PCA o”
Arbitrage-free SVI volatility surfaces (2012, background): “There has been some work on arbitrage-free interpolation of implied volatilities or equivalently of option prices [1], [11], [16], [21].”