What Goes into Risk-Neutral Volatility? Empirical
Estimates of Risk and Subjective Risk Preferences

Abstract

Under Black–Scholes (BS) assumptions, empirical volatility and risk-neutral volatility are given by a single parameter that captures all aspects of risk. Inverting the model to extract implied volatility from an option’s market price gives the market’s forecast of future empirical volatility. But real world returns are not lognormal, volatility is stochastic, and arbitrage is limited; thus, option prices embed both the market’s estimate of the empirical returns distribution and also investors’ risk attitudes, including possibly distinct preferences over different volatility-related aspects of the returns process, such as tail risk. All these influences are reflected in the risk-neutral density (RND), which can be extracted from option prices without requiring restrictive assumptions from a pricing model. The author computes daily RNDs for the S&P 500 Index over 15 years and finds that risk-neutral volatility is strongly influenced both by investors’ projections of future realized volatility and by the risk-neutralization process. Several significant variables are connected in different ways to realized volatility, such as the daily trading range and tail risk; others reflect risk attitudes, such as the level of investor confidence and the size of recent volatility forecast errors.