Robust Estimation of Shape-Constrained State Price Density Surfaces

摘要

In order to better capture empirical phenomena, research on option price and implied volatility modeling increasingly advocates the use of nonpara-metric 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.