A New Nonparametric Estimate of the Risk-Neutral Density with Applications to Variance Swaps

Abstract: We develop a new nonparametric approach for estimating the risk-neutral density of asset prices and reformulate its estimation into a double-constrained optimization problem. We evaluate our approach using the S&P 500 market option prices from 1996 to 2015. A comprehensive cross-validation study shows that our approach outperforms the existing nonparametric quartic B-spline and cubic spline methods, as well as the parametric method based on the Normal Inverse Gaussian distribution. As an application, we use the proposed density estimator to price long-term variance swaps, and the model-implied prices match reasonably well with those of the variance future downloaded from the CBOE website.