State price density estimation for options with dividend yields

Option pricing is a challenging issue that requires the fulfilment of many assumptions. The market practice for the pricing of illiquid options is often based on the usage of implied volatilities of liquid options for the construction of a so-called volatility surface. Since the surface is obtained by interpolation and a smoothing procedure, it might break the no-arbitrage condition of positive state price densities or price relations. In this paper,we extend our previous works and focus on the pricing of selected options on dividend-paying stocks traded on the German market. In particular, we construct the implied volatility surface for a large selection of combinations of time-to-maturity and moneyness, calculate state price densities and analyse the behaviour in different time grids.