What Does Today’s Smile Imply About Future Volatilities?

Abstract

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 investing

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 are identified.

• • 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.