Risk Neutral Density Functions for the S&P500 and the COVID-19 Pandemic

This paper takes conclusions on markets expectations by analysing risk-neutral density (RND) functions on options of the Standard and Poor’s 500. After a review of the literature on this subject a parametric approach is proposed to estimate RND functions, a two lognormal technique. The descriptive statics on the RND functions allow to conclude a pattern that seems to be in line with much of the work on the subject. When distressed periods arise there is an increase in left skewness, a decrease in kurtosis and volatility is generally higher. It comes to the conclusion that markets had difficulties in understanding the full economic impact of the pandemic. In this shock period, investors were not able to adapt their perspectives on the future path of monetary policy. The results show they barely anticipated the decisions of monetary policy agents or other officials, changing beliefs as authorities altered stance. Several are the applications proposed on this paper for the use of RND functions.