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

Estimates of risk-neutral densities future asset returns have been commonly used for pricing new financial derivatives, detecting profitable opportunities, and measuring central bank policy impacts. We develop a nonparametric approach estimating the density prices reformulate its estimation into double-constrained optimization problem. evaluate our using S&P 500 market option from 1996 to 2015. A comprehensive cross-validation study shows that outperforms existing quartic B-spline cubic spline methods, as well parametric method based on normal inverse Gaussian distribution. As an application, we use proposed estimator price long-term variance swaps, model-implied match reasonably with those downloaded Chicago Board Options Exchange website.