On the Skew Stickiness Ratio

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 Itô-Wentzell and Clark-Ocone formulae, and we apply it to analyze its asymptotics under Bergomi-type stochastic volatility models.

💡 Research Summary

The paper provides a rigorous mathematical treatment of the Skew Stickiness Ratio (SSR), a statistic designed to capture the joint dynamics of an asset price and its volatility. The authors begin by modeling the asset price (S_t) as a stochastic differential equation (dS_t = S_t\sqrt{V_t},dB_t), where (V_t) is a positive, continuous, adapted variance process and (B) is a standard Brownian motion. They define the put option price process (P_t(K)) and the implied total variance (\Sigma_t(K)) through the Black‑Scholes formula, and introduce the at‑the‑money implied volatility (\sigma_t(K)=\Sigma_t(K)\sqrt{T-t}). The SSR is then defined as
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