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 these methods require dense observations to yield sensible results. Calibration is therefore typically performed using time-series data. Ironically, the use of historical 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 only a snapshot of option prices. Our estimators are genuinely conditional 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