PT - JOURNAL ARTICLE AU - Riccardo Rebonato TI - What Does Today’s Smile Imply About Future Volatilities? AID - 10.3905/jod.2019.1.091 DP - 2019 Nov 15 TA - The Journal of Derivatives PG - jod.2019.1.091 4099 - https://pm-research.com/content/early/2019/11/15/jod.2019.1.091.short 4100 - https://pm-research.com/content/early/2019/11/15/jod.2019.1.091.full AB - This article presents a simple and financially justifiable way to extract the evolution of the smile surface in the (ℚ) measure from today’s plain vanilla option prices. By combining this information with (ℙ)-measure estimation of the dependence of implied volatility on the underlying, one can 1) obtain information about the existence and magnitude of a volatility risk premium; 2) devise trading strategies; and 3) price options such as Forward Volatility Agreements (FVAs). TOPICS: Options, analysis of individual factors/risk premia, factor-based models, style investingKey Findings• Plain vanilla smiles of different maturities are compatible with an infinity of future smiles, but these are linked by strong consistency relationships, which we identify.• Using these consistency relationships and very mild assumptions, we obtain the future smiles that are most compatible with space and time homogeneity and price today’s plain-vanilla options.• There is an interesting discrepancy between the dependence of ATM volatilities in the future smiles so obtained and the empirical dependence of the same quantity.