A New Nonparametric Estimate of the Risk-Neutral Density with Applications to Variance Swaps - Jiang, Liyuan; Zhou, Shuang; Li, Keren; Wang, Fangfang; Yang, Jie (Frontiers in Applied Mathematics and Statistics, 2021)
Estimates of risk-neutral densities of future asset returns have been commonly used for pricing new financial derivatives, detecting profitable opportunities, and measuring central bank policy impacts. 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.