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

TL;DR

This paper introduces a novel nonparametric method for estimating the risk-neutral density of asset prices, improving accuracy over existing methods and effectively pricing variance swaps using market data.

Contribution

The paper presents a new nonparametric estimation technique reformulated as a double-constrained optimization, outperforming prior methods in accuracy and application to variance swap pricing.

Findings

Outperforms existing nonparametric and parametric methods in density estimation.

Provides accurate pricing of long-term variance swaps.

Model-implied prices align well with market data.

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.