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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.

The authors provide new evidence in favor of the expectation hypothesis (EH) as a long-run theory of the term structure of interest rates. Using nonparametric techniques first, the authors show that the results of conventional tests that reject EH are strongly affected by the presence of extreme observations – only a handful in the case of longer maturities. The authors then provide a new general methodology that determines the number of outliers causing any theory to fail, and their approach quantifies the extent of this failure.