Risk Neutral Density Estimation with a Functional Linear Model

Abstract

This chapter proposes a nonparametric estimator of the risk neutral density (RND) based on cross-sectional European option prices. The authors recast the arbitrage-free equation for option pricing as a functional linear regression model where the regressor is a curve and the independent variable is a scalar corresponding to the option price. Then, the authors show that the RND can be viewed as the solution of an ill-posed integral equation. To estimate the RND, the authors use an iterative method called Landweber-Fridman (LF). Then, the authors establish the consistency and asymptotic normality of the estimated RND. These results can be used to construct a confidence interval around the curve. Finally, some Monte Carlo simulations and application to the S&P 500 options show that this method performs well compared to alternative methods.

Citation

Carrasco, M. and Tsafack, I. (2023), "Risk Neutral Density Estimation with a Functional Linear Model", Chang, Y., Lee, S. and Miller, J.I. (Ed.) Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications (Advances in Econometrics, Vol. 45B), Emerald Publishing Limited, Leeds, pp. 133-157. https://doi.org/10.1108/S0731-90532023000045B005