Evaluating implied RNDs by some new confidence interval estimation techniques

Abstract

This paper evaluates the precision of the parametric double lognormal and the non-parametric smoothing spline method for estimating risk-neutral distributions (RNDs) from observed option prices. By using a bootstrap technique, confidence bands are estimated for the risk-neutral distributions and the width of the confidence bands is used as a criterion when evaluating the precision of the two methods. Previous literature on estimating confidence bands has to a large extent been estimated using Monte Carlo methods. This paper argues that the bootstrap technique is to be preferred due to the non-normality feature of the error structure. Furthermore, it is shown that the inclusion of a heteroscedastic error structure improves the precision of the estimated RNDs. Our findings favour the smoothing spline method as it produces tighter confidence bands. In addition, an example of how to apply the estimated confidence bands in practice is also provided.