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Risk Neutral Density Estimation with a Functional Linear Model

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

Author

Listed:
  • Marine Carrasco
  • Idriss Tsafack

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.

Suggested Citation

  • Marine Carrasco & Idriss Tsafack, 2023. "Risk Neutral Density Estimation with a Functional Linear Model," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications, volume 45, pages 133-157, Emerald Group Publishing Limited.
    • Handle: RePEc:eme:aecozz:s0731-90532023000045b005
    DOI: 10.1108/S0731-90532023000045B005
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