Risk Neutral Density Estimation with a Functional Linear Model

Marine Carrasco and Idriss Tsafack

A chapter in Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications, 2023, vol. 45B, pp 133-157 from Emerald Group Publishing Limited

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.

Keywords: Risk neutral density; option pricing; regularization; functional regression; Landweber-Fridman; nonparametric (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eme:aecozz:s0731-90532023000045b005

DOI: 10.1108/S0731-90532023000045B005

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