Comparison of methods to estimate option implied risk-neutral densities

Abstract

This paper is a comparison study of non-parametric techniques used to estimate risk-neutral densities from option prices. Cross-sectional option prices are first generated using Monte Carlo simulation. Using these simulated options data, risk-neutral densities of the underlying asset are estimated using three different non-parametric methods. The performances of these non-parametric estimation methods are then evaluated by comparing the estimated densities with the theoretical density. Unlike previous comparison studies that use traded options data without knowing the true risk-neutral densities, this study uses simulated option data with known data-generating processes and their corresponding risk-neutral densities, hence giving a real evaluation of the non-parametric estimation methods. This study finds that the kernel regression method yields the best performance, followed by the spline interpolation method and the neural network models.