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

Frontiers in Applied Mathematics and Statistics

Shuang Zhou¹  Liyuan Jiang¹  Jie Yang¹  Keren Li¹  Fangfang Wang² 

[1] Chicago, IL, United States;Worcester, MA, United States;

关键词: pricing;    risk-neutral density;    double-constrained optimization;    normal inverse Gaussian distribution;    variance swap;   

DOI  :  10.3389/fams.2020.611878

来源: Frontiers

【 摘 要 】

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 Chicago Board Options Exchange website.

【 授权许可】

CC BY