Long and Short-Term Dynamics of the S&P500 Option-Implied Distribution

Abstract

We propose a modelling treatment for the option-implied risk neutral distribution (RND) which disaggregates its long-term and short-term dynamics. Long memory parameters calibrated on the RND moments serve as tractable mathematical constructs to filter out effects of smooth structural change related to investor risk aversion and macroeconomic influence; the remaining short-term effects relate to changes in investors’ objective probability distribution of future prices on the underlying asset. Time series measures of the long-term and short-term moment dynamics are separately studied in vector auto regressions. Asymmetry and tail expectations are found to be subsumed in volatility expectations and significant co-moment interactions are found in the higher-order moments. The proposed model outperforms recently proposed vector alternatives for forecasting the RND, particularly skewness and kurtosis.