Smooth and bid-offer compliant volatility surfaces under general dividend streams

Given bid-offer quotes for a set of listed vanilla options, a fundamental need of option market makers is to interpolate and extrapolate the available quotes to a full arbitrage-free surface. We propose a methodology which directly controls the trade-off between smoothness and bid-offer compliance of the resulting volatility surface. Unlike previous literature, the method applies simultaneously to all listed maturities and aims to smooth the implied risk neutral densities. Additionally, we consider asset dynamics which allow for general dividend streams - continuous, discrete yield and discrete cash - a modeling aspect of key importance in option markets