  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.
