On the Skew Stickiness Ratio

Battle Count: 77

The SSR is a critical statistic for derivative hedging, particularly for managing cross gamma risk in stochastic volatility models. The paper provides the first rigorous derivation of the SSR formula, which is essential for model calibration and hedging. The empirical SSR values (~3/2 for Euro Stoxx 50 and S&P 500) directly impact trading strategies involving options. The asymptotic results help traders understand how SSR behaves in different market regimes (short maturity, low vol-of-vol). However, the paper is theoretical and does not provide direct trading signals or strategies.

The paper requires advanced knowledge of stochastic analysis (Itô-Wentzell formula, Clark-Ocone formula, Malliavin calculus, martingale representation theorem), functional analysis, and asymptotic methods. Implementing the SSR formula in practice would require computing Malliavin derivatives of the asset price process, which is non-trivial. The Bergomi-type model framework with multiple correlated Brownian motions adds further complexity. The theoretical results are not directly implementable without significant additional work to connect them to numerical methods.

The paper is purely theoretical with complete mathematical proofs. All derivations are self-contained and verifiable. However, there is no code, no numerical experiments, and no empirical data provided in this extract. Reproducibility depends on the reader's ability to verify the mathematical proofs. The asymptotic results (Theorems 3 and 4) are analytical and can be independently verified.