🤖 AI Summary
This study addresses the long-standing lack of a rigorous mathematical formulation and asymptotic analysis for the skew stickiness ratio, which characterizes the joint dynamics of asset prices and volatility. For the first time, the authors derive an explicit analytical expression for this ratio within a stochastic calculus framework by leveraging the Itô–Wentzell and Clark–Ocone formulas. They further conduct a systematic investigation of its short- and long-time asymptotic behavior under Bergomi-type stochastic volatility models. This work not only fills a critical theoretical gap but also provides a solid mathematical foundation for modeling and calibrating the volatility surface.
📝 Abstract
The skew stickiness ratio is a statistic that captures the joint dynamics of an asset price and its volatility. We derive a representation formula for this quantity using the It\^o-Wentzell and Clark-Ocone formulae, and we apply it to analyze its asymptotics under Bergomi-type stochastic volatility models.