Rough Volatility, Forward Variance Geometry, and the Non-Markovian Shape of Short-Horizon Risk

We re-examine the geometry of the forward variance curve under rough volatility specifications with Hurst index H well below one half. The persistence of negative skew at short maturities is reconstructed as a consequence of the non-Markovian kernel structure rather than a leverage parameter, with practical consequences for the stability of vanna and the interpretability of short-dated risk-reversals around scheduled event windows.

Let v_t denote instantaneous variance with v_t = ξ_0(t) + ∫_0^t K(t−s) η(v_s) dW_s where K(τ) ≈ τ^{H−1/2}. Calibration is interpreted as identification of the forward variance functional ξ_0(·) jointly with the kernel exponent H.

The mapping between observed implied volatility surfaces and rough volatility parameterizations is not topologically trivial: small perturbations in the short-maturity smile can induce non-local rearrangements of the forward variance functional. In practical terms, fitting a single day of options data without temporal regularization tends to absorb microstructure noise into ξ_0(·), inflating apparent term-structure curvature.

Short-horizon directional research that conditions on implied volatility regime should treat single-snapshot calibrations as point estimates of a poorly-conditioned inverse problem. We prefer ensemble parameterizations with explicit penalization on temporal variation of ξ_0(·).

The commentary does not address jump components or rough-Heston extensions where the variance process retains an affine structure under integral representations. Empirical assertions reference published surfaces and are not derived from proprietary data.