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.

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今天的微笑对未来的波动意味着什么？

本文提供了一种简单且经济合理的方法，可从当今的普通香草期权价格中以（ℚ）度量来提取微笑面的演变。通过将此信息与隐含波动率对底层证券的依赖关系的（ℙ）度量估计相结合，人们可以1）获得有关波动率风险溢价的存在和程度的信息；2）制定交易策略；3）价格选择，例如远期波动率协议（FVA）。主题：选项，对单个因素/风险溢价的分析，基于因素的模型，风格投资主要发现•不同成熟度的普通香草微笑与无限的未来微笑兼容，但是这些与强一致性关系相关联，已被确定。•使用这些一致性关系和非常温和的假设，我们获得了与时空同质性和当今普通香草价格最兼容的未来笑容。•在如此获得的未来微笑中，ATM波动率的依赖性与相同数量的经验依赖性之间存在有趣的差异。