Beyond the Skew-Stickiness Ratio: Transport Geometry of Spot-Driven Variance Surface Dynamics¶
Bibliographic record. Follow the original-source link for the publication.
| Field | Value |
|---|---|
| Primary domain | Volatility |
| Other domains | — |
| Methods | Research Methods |
| Facets | — |
| Authors | Charlie Che, Pradeepta Das |
| Published | 2026-08-12 |
| Source | arXiv Quantitative Finance History |
| Identifiers | arxiv:2608.12493 |
| URL | Open original source |
Editorial synthesis¶
Why it matters¶
This preprint organizes SSR's scalar ride-speed into local velocity jets for a spot-driven total-variance surface, with testable level, skew and curvature response equations. Its options-research value is explicit local conditions and an SPX benchmark, not proof of global arbitrage freedom, complete joint volatility dynamics or trading returns. (full_text:S1, full_text:S24, full_text:S26, full_text:S228, full_text:S381, full_text:S453, full_text:S527, full_text:S609, full_text:S610, full_text:S634)
Main author claims¶
- The authors express transport as ∂u w = v ∂k w and derive the first three surface-jet response equations using total k-derivatives β, η and ψ of the composite velocity. Their v=0, v=1 and constant-β cases correspond to sticky-delta, sticky-strike and SSR. A single trajectory identifies composite velocity, not separate explicit-k and w-dependence contributions. (
full_text:S24,full_text:S25,full_text:S26,full_text:S224,full_text:S226,full_text:S227,full_text:S228,full_text:S234) - The authors report: Theorem 6.6 claims preservation of strict static admissibility over a sufficiently small spot-perturbation interval when initial calendar and butterfly densities have uniformly positive margins and pointwise velocity and initial surface satisfy the V1-V3/W regularity and boundedness conditions. This is a conditional local result; the authors explicitly make no global arbitrage-preservation claim. (
full_text:S78,full_text:S381,full_text:S382,full_text:S383,full_text:S384,full_text:S385,full_text:S607,full_text:S608,full_text:S610) - The authors report ATM β declining from 1.4375 at 1M to 1.0114 at 24M, rejection of η=ψ=0 at all seven tenors, and primary smooth-trend rejection of β strike-constancy at 2M-12M but not 1M/24M. In five-fold blocked CV on real SPX data, Full-model curvature-change RMSE improves 17-21% over SSR at 3M/6M, without comparable full-smile improvement. (
full_text:S462,full_text:S470,full_text:S476,full_text:S506,full_text:S508,full_text:S512,full_text:S527,full_text:S529,full_text:S534,full_text:S536)
Data, method, or discussion scope¶
Variables are w=σ²T, k=log(K/F) and u=log F; cubic-fit a0-a3 and observed Δu describe Δa0-Δa2. SPX data span 2021-07-12 to 2026-07-09, with 1118 usable observations per tenor after |Δu|≥0.001 and fit R²≥0.95 filters, seven 1M-24M tenors, eleven K/F=0.85-1.15 points and seven local centers. Reporting includes 60-day rolling diagnostics, HC3, 500-resample pairs/block bootstraps and a primary two-contrast Wald addressing near-singular cross-strike covariance. Empirical CV compares random walk, SSR, SSR+skew and Full on jet-change and smile RMSE. Separate 500-trial fixed-design block-residual DGP validation explicitly does not establish that SPX follows the model. (full_text:S53, full_text:S54, full_text:S119, full_text:S453, full_text:S454, full_text:S455, full_text:S456, full_text:S457, full_text:S458, full_text:S459, full_text:S460, full_text:S461, full_text:S468, full_text:S503, full_text:S504, full_text:S505, full_text:S506, full_text:S527, full_text:S528, full_text:S529, full_text:S554, full_text:S557, full_text:S558, full_text:S560)
Main limitations¶
Author-stated limits include unanalysed wing-growth conditions, exclusion of nonlocal local-volatility velocity from the main theorem, and deferred maturity-direction dynamics, global compatibility of local jets, rigorous manifold foundations and complete operator classification. Near-zero ATM skew at 1M and off-ATM higher-order jets cause weak identification/large SEs. Reader-inferred untested boundaries: cubic fits and tenor-wise regressions do not verify all theorem conditions for the empirical field; spot-response regression is not a joint market model with independent volatility shocks or a dynamic no-arbitrage guarantee. Held-out regressions use contemporaneously observed Δlog F, but fold/input chronology is unspecified; this is not proof of leakage and does not validate forecasting using only information available at the prediction origin. The 17-21% gain is specifically 3M/6M curvature versus SSR: Table 7 has lower random-walk curvature RMSE than Full at 1M/3M and slightly higher Full smile RMSE than SSR at 6M/12M. Hedging P&L, trading costs and tradable economic gains are not tested. (full_text:S83, full_text:S84, full_text:S85, full_text:S226, full_text:S227, full_text:S304, full_text:S307, full_text:S382, full_text:S384, full_text:S414, full_text:S415, full_text:S456, full_text:S459, full_text:S521, full_text:S526, full_text:S527, full_text:S528, full_text:S529, full_text:S534, full_text:S536, full_text:S540, full_text:S574, full_text:S601, full_text:S602, full_text:S609, full_text:S610, full_text:S615, full_text:S627, full_text:S628, full_text:S632, full_text:S634)
Relationships¶
- None recorded.