The Journal of Derivatives, Vol. 27, Issue 2, Winter 2019
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).
Key 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.