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....

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....

Trading in options with a wide range of exercise prices and a single maturity allows a researcher to extract the market's risk neutral probability density (RND) over the underlying price at expiration. The RND contains investors' beliefs about the true probabilities blended with their risk...