Recovering Risk-Neutral Densities: A New Nonparametric Approach

Abstract

This paper proposes a novel nonparametric method to recover the implied risk-neutral density (RND) from option prices. The main advantages of this method are that it 1) is almost completely agnostic about the true underlying process, 2) controls against overfitting while allowing for small samples, 3) always results in sensible arbitrage-free distributions, 4) estimates the RND over the observable range of strikes only, without involving any extrapolation of density in the tails, 5) is computationally very simple, and 6) can be used to estimate multivariate RNDs. In an empirical application, the new method is implemented on the S&P Index options data over the period from 1991 to 1995. To characterize shapes of the Index's RNDs the paper uses the percentile moments which overcome unobservability of the tails of a distribution. The implied RNDs exhibit persistent negative skewness and excessive peakedness. The departures from lognormality become more pronounced as option maturity increases. Day-to-day variation of the RNDs is found to be related to the recent performance of the Index. In particular, on trading days when the Index declines the implied RNDs are more skewed and peaked than when the Index advances. Finally, the implied probabilities of extreme outcomes are also estimated.