A soybean desk can use these smile indicators, but the paper has yet to show that they price soybean options. Tchoneteck, Zhang and Viens make a convincing case for giving level, skew and convexity separate dynamics. The step from those indicators to usable pricing states is much less convincing. Every pricing check compares the model with itself, while the vol-of-vol passed to the pricer is nearly the same across regimes.

From CVOL to a price

CME publishes soybean-option CVOL indicators each day after the CBOT close: 30-day ATM vol, upside and downside variance, and a 30-day total variance field (Var30). The authors derive four indicators. Three enter the pricer: L is ATM vol; S is additive skew, measured as upside minus downside variance in vol points; and C is Var30 divided by ATM vol, with values above 1 indicating extra variance in the wings. The fourth, skew ratio R, correlates 0.951 with S. Their sample covers October 1, 2013 to August 26, 2025, or 2,998 trading days without gaps.

The futures model gives log-volatility mean reversion (log-OU), vol-of-vol ξ and futures-vol correlation ρ. Leading-order smile relations connect L with spot vol σ, C minus 1 with ξ², and S with ρξσ. Applied each day, those relations produce surface-implied vol-of-vol and leverage in place of constant parameters. The authors regularize both, then hold them fixed over each option's life. They price options by Monte Carlo, cross-check the PDE with Crank-Nicolson finite differences, and train a neural network on 8,640 Monte Carlo-labelled contracts for faster pricing. The proposed trading use is regime pricing: in the La Niña window, model prices exceed the full-sample benchmark by 37.66%, with implied vol 298.30 bps higher.

Skew needs its own process

The empirical case holds up. For ATM level, log-OU beats CIR by 195.1 AIC points and OU by 576.8. It also wins for skew ratio, by 124.6 over CIR, and convexity, by 45.2 over CIR. Additive skew takes a negative value on 434 of 2,998 days (14.5%). That sign change forces OU rather than CIR or log-OU. The indicators also decay at different rates: half-lives are 24.0 trading days for level, 15.1 for skew and 7.1 for convexity. Level and convexity correlate at -0.230; as ATM vol rises, the smile tends to flatten in relative terms.

There are cracks, which the authors flag. KPSS rejects stationarity for skew (p=0.019) and convexity (p<0.010); they attribute this to regime shifts. The stationary model also misses the seasonal pattern. July ATM vol averages 22.7% against 16.5% in February, while July skew is 4.41 against 0.83 in October.

What does a z of 45 on vol-of-vol equality reject?

The ATM level's time-series log-OU vol-of-vol is 0.842. Convexity implies a mean of 2.543. A Newey-West equality test gives z of about 45.3 with a 20-day bandwidth, and between about 25 and 78 over the bandwidths tried. The authors say the gap "should not be read as a pure failure of the physical-measure model." Time-varying vol-of-vol, volatility risk premia, jumps or approximation error could account for it. Their narrower claim, that curvature contains information absent from ATM level, is persuasive. The test itself does not identify where the gap comes from.

Approximation error warrants more attention. In the paper's exact formulation, skew and convexity are the first and second derivatives of implied vol at zero log-moneyness, with equivalent finite-difference definitions matching the CVOL construction. The closed-form recovery formulas use a narrower link: Gram-Charlier cumulants are mapped to at-the-money smile slope and curvature coefficients. CVOL's S measures a variance difference, while C divides Var30 by ATM vol. The paper does not show that UpVar30 minus DnVar30, or Var30 divided by ATM vol, equals those coefficients. It gives the fourth-cumulant step one sentence (κ₄ = O(ξ²)). For a rigorous treatment of both cumulant steps, the authors write, "we do not reproduce that full expansion here."

The cap then removes much of the apparent vol-of-vol variation. Raw surface vol-of-vol averages 2.54 in the full sample, 2.65 in the COVID window and 2.78 in the La Niña window. The corresponding pricing values after the cap are 1.20, 1.19 and 1.20. Means of 1.19 to 1.20 beside raw means of 2.54 to 2.78 suggest a binding cap. We did not find the value of either cap, on vol-of-vol or leverage, in the paper. Leverage does vary across regimes: mean ρ^Q is 0.394, 0.658 and 0.642, and σ is 0.188 against 0.292 for La Niña. Mean reversion κ = 6.651 passes unchanged from the physical fit into the risk-neutral model.

The Monte Carlo checks

At 180 days, mean absolute relative error against Monte Carlo is about 0.10% for finite differences and 0.35% for the network. The authors explain the 19.8% error at 30 days and K/F0 = 1.20 by its Monte Carlo price of 0.146. Still, finite differences and the network both price that contract about 20% above Monte Carlo, in the same direction as the other gaps.

Some differences exceed sampling noise. At 30 days and K/F0 = 1.10, finite differences and Monte Carlo differ by 0.073 against a standard error of 0.023. At 90 days and 1.20, the difference is 0.134 against 0.056. The grid contains only 15 contracts.

Dates mix within regimes in the network's random 70/15/15 split of Monte Carlo labels. Its reported 5,059.59x speed-up, at 0.000188 seconds per option, measures inference after training, as the paper states.

The authors describe the three-way agreement as a check on internal numerical consistency. The abstract goes further, saying the results "support the use of level, skew, and convexity jointly as dynamic inputs for commodity-option pricing." We did not find a comparison with observed soybean option quotes or settlements. Nor did we find the hedging results that the conclusion points to in Section 4 and Appendix B. The La Niña and COVID impacts come from model outputs on five representative dates per window; we did not find how those dates were selected. The COVID price impact of -12.45% is consistent with lower mean ATM vol in that window, 17.64% against 18.60%, although the impact comes from five dates rather than the window average.

A desk diagnostic

The empirical work gives a soybean desk a reason to track skew with its own sign-changing process. Its 7.1-day convexity half-life also offers a rough decay prior for wing marks. That 7.1-day figure is a lag-1 proxy, and the paper notes that convexity may have a second, slower timescale. The identification formulas are cheap enough for a daily read on implied leverage.

We could not test any of this ourselves. The exercise requires the CME CVOL indicator series, which we do not hold. Soybean futures prices alone provide realized vol and cannot reproduce the smile-based identification.

Model prices using the surface-implied states, compared with soybean option settlements on the 85 La Niña days, would change my view.