Do Stochastic Volatility and/or Jumps Improve the Consistency of Risk-Neutral Distributions Implicit in the S and P 500 Index Option Market and the Cash Index Market

Abstract

This paper examines the relative importance of stochastic volatility and price jumps in option pricing by exploiting the differences in option-based and index return-based risk-neutral densities. As evinced by the persistent smirked volatility smile, this study extracts the risk-neutral densities by exploiting the information embedded in the implied volatilities that are smoothed by a kernel regression. On the other hand, a canonical valuation approach is adopted to identify the risk-neutral density from the observed index returns. Statistical tests and implied risk aversion are constructed to investigate the differences between two risk-neutral densities. The 30-day S&P 500 options under stochastic volatility are found efficiently priced. By using a longer horizon of underlying returns, however, we are able to partly reconcile the differences between the index and option-implied risk-neutral densities after adding a jump component to the index dynamics. Option investors are found more risk averse than stock traders except for the 30-day jump-diffusion with stochastic volatility. The finding may help illustrate the puzzle that implicit volatilities are greater than subsequent realized volatilities.