What is Risk Neutral Volatility?

Abstract

Under Black-Scholes (BS) assumptions, empirical volatility and risk neutral volatility are given by a single parameter, which 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, so option prices embed both the market's estimate of the true returns distribution and also investors' risk attitudes, including possibly different preferences over specific volatility-related aspects of the returns process, such as tail risk. Using options with a dense set strikes, we can obtain the entire risk neutral density (RND) which reflects all of these influences without requiring restrictive assumptions from a pricing model.We compute daily RNDs for the SP others are meant to reflect risk attitudes, such as the level of investor confidence and the size of recent volatility forecast errors. As a forecast of future volatility, RND volatility fully impounds the information in historical volatility, but not a more sophisticated GARCH forecast, and its forecasting power seems greatest in the range of 1 to 2 weeks ahead.