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Risk Neutral Density Estimation with a Functional Linear Model

Marine Carrasco (Economics Department, University of Montreal, Montreal, Quebec, Canada)

Idriss Tsafack (Economics Department, University of Montreal, Montreal, Quebec, Canada)

Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications

ISBN: 978-1-83753-213-1, eISBN: 978-1-83753-212-4

Publication date: 24 April 2023

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

Acknowledgements

Acknowledgment

The authors thank the editor and referees for their useful comments. Carrasco thanks NSERC for partial financial support.

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

Publisher

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Emerald Publishing Limited