@article {Rebonatojod.2019.1.091, author = {Riccardo Rebonato}, title = {What Does Today{\textquoteright}s Smile Imply About Future Volatilities?}, elocation-id = {jod.2019.1.091}, year = {2019}, doi = {10.3905/jod.2019.1.091}, publisher = {Institutional Investor Journals Umbrella}, abstract = {This article presents a simple and financially justifiable way to extract the evolution of the smile surface in the (ℚ) measure from today{\textquoteright}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{\textbullet} 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.{\textbullet} 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{\textquoteright}s plain-vanilla options.{\textbullet} 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.}, issn = {1074-1240}, URL = {https://jod.pm-research.com/content/early/2019/11/15/jod.2019.1.091}, eprint = {https://jod.pm-research.com/content/early/2019/11/15/jod.2019.1.091.full.pdf}, journal = {The Journal of Derivatives} }