Arbitrage-free smoothing of the implied volatility surface

Abstract

The pricing accuracy and pricing performance of local volatility models depend on the absence of arbitrage in the implied volatility surface. An input implied volatility surface that is not arbitrage-free can result in negative transition probabilities and consequently into mispricings and false greeks. We propose an approach for smoothing the implied volatility smile in an arbitrage-free way. The method is simple to implement, computationally cheap and builds on the well-founded theory of natural smoothing splines under suitable shape constraints.