Robust Estimation of Shape Constrained State Price Density Surfaces

In order to better capture empirical phenomena, research on option price and implied volatility modeling increasingly advocates the use of nonparametric methods over simple functional forms. This, however, comes at a price, since they require dense observations to yield sensible results. Calibration is therefore typically performed using aggregate data. Ironically, the use of time-series data in turn limits the accuracy with which current observations can be modeled. We propose a novel approach that enables the use of flexible functional forms using daily data alone. The resulting estimators yield excellent fits and generalize well beyond available data, all the while respecting theory imposed shape constraints. We demonstrate the numerical stability and the pricing performance of our method by approximating arbitrage-free implied volatility, price and state price density surfaces from S&P 500 options over a period of 12 years.