Tail-Driven Nonparametric Estimation for State Price Densities

This paper proposes and implements a novel nonparametric method for estimating the state price density (SPD) over the entire state space, including the tails. This SPD estimator achieves shape consistency properties in theory, particularly at the tails. Monte Carlo simulations demonstrate the accuracy and robustness of our method. In particular, our estimator accurately captures the risk-neutral tail distribution, which is often underestimated by existing alternative methods. In an empirical analysis based on Standard and Poor’s 500 options data, we evaluate the out-of-sample performance of our SPD estimation method and demonstrate that the estimates can serve as effective indicators for market conditions and exhibit predictive power for asset returns. Combining these perspectives, we suggest that our SPD estimator renders a valuable tool for risk management and asset pricing. This paper was accepted by Kay Giesecke, finance. Funding: The research of C. Li was supported by the Guanghua School of Management, the Center for Statistical Science, the High-Performance Computing Platform, and the Key Laboratory of Mathematical Economics and Quantitative Finance (Ministry of Education) at Peking University as well as the National Natural Science Foundation of China [Grant 72173003]. The research of X. Song was supported by the Guanghua School of Management, the Center for Statistical Science, and the Key Laboratory of Mathematical Economics and Quantitative Finance (Ministry of Education) at Peking University as well as the National Natural Science Foundation of China [Grants 72373007 and 72333001]. The research of Y. Wan was supported by the School of Management Science and Engineering and the Coordinated Innovation Center for Computable Modeling in Management Science at Tianjin University of Finance and Economics as well as the Tianjin Municipal Education Commission [Grant 2022SK188]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.03236 .