A forecast below 0.273 annualized puts every stock in the moneyness-led group; at 0.303 or above, maturity leads every time. Mu'azara and Artiono associate the stock-level differences with each stock's GJR-GARCH volatility input and with factor interactions. Their parameter and dominant-factor tables make the divide exact. It is the paper's most useful result, and a measure of how much the headline ranking depends on the experiment's design.

The prices being decomposed

The authors study 19 stocks that remained in a masked Indonesian blue-chip index, Index X, through every official evaluation from February 2022 to December 2025. Each has 937 adjusted closes and 936 daily log returns, covering 2022-02-02 to 2025-12-30. Selecting continuous constituents introduces potential survivorship bias, as the authors acknowledge. They fit each stock with a GJR-GARCH(1,1), whose variance can respond more strongly to negative shocks when the data support it. The model uses a constant mean and normal innovations. Its one-day-ahead volatility forecast is annualized by the square root of 252, then held fixed.

That fixed forecast goes into a Black-Scholes call. For each stock, the authors draw five inputs independently and uniformly across 7,168 scenarios:

A Sobol total-order index assigns each input a share of output variance, including its interactions. Across stocks, the baseline averages are 0.468080 for maturity and 0.455075 for moneyness. The multiplier receives 0.082025, the rate 0.003616 and the cost loading 0.000225. The paper says: "The difference is only 0.013005, so these two factors are better described as jointly dominant."

There are no option quotes in the test. The authors explicitly call it "not evidence of improved pricing accuracy against observed option prices." These indices decompose the variance of a closed-form price, with nothing to trade. The numerical calculation is steady: maturity's index is 0.467842, 0.468080 and 0.468069 at N = 512, 1024 and 2048.

Who set the ranges?

The analyst chose them. In the paper's formulation, the call equals S0 times a function of q, T, r and effective volatility. Normalization removes spot price from the indices. What remains to determine the ranking is the chosen set of bounds alongside each stock's fixed volatility forecast.

Widen the domain and the order changes. Moneyness now covers [0.85, 1.15], maturity reaches 1.5 years and the multiplier covers [0.50, 1.50]. Moneyness leads at 0.456509; maturity drops to 0.364628. The multiplier moves from 0.082025 to 0.193912, about 2.4 times as large. Its half-width doubled, though the other ranges widened too, so that increase cannot be assigned to the multiplier range alone.

The authors concede that "magnitudes and ordering are conditional on the scenario domain." Their narrower claim holds: for this response, over these ranges, contract terms lead. A trader gets little from that claim alone. It describes how a Black-Scholes call reacts to the selected inputs.

The stock-level divide

The ten moneyness-led stocks have forecast vols between 0.197550 (Stock O) and 0.272773 (Stock N). For the nine maturity-led stocks, the range is 0.303241 (Stock R) to 0.670147 (Stock J). Stock J has the paper's largest single-stock index, 0.712622 for maturity. Stock O, with the lowest forecast vol, has a moneyness index of 0.661237.

Black-Scholes supplies the mechanism. Time value scales with sigma times root T. At high sigma, extending maturity from one month to one year outweighs a ±10% strike shift; at low sigma, the strike shift has the larger effect.

The Student-t check runs in the same direction. Student-t innovations beat normal innovations on AIC for all 19 stocks, although the authors retain the normal baseline. They say the comparison supports that baseline without making its exact Sobol magnitudes universal. Student-t innovations increase forecast vol for 17 of 19 stocks. Aggregate maturity then rises to 0.489742, while moneyness falls to 0.427795.

Each stock's label follows a one-day forecast fixed on a single date: none below 0.273 is maturity-led, and none above 0.303 is moneyness-led. The authors acknowledge that using that forecast for maturities up to a year does not produce a horizon-consistent GJR-GARCH price. Their reason for freezing it is to isolate contract inputs under one information set. Allowing volatility to change with T would entangle maturity with variance dynamics. Yet the fixed volatility level decides which contract factor leads.

Stock N (0.272773) and Stock R (0.303241) lie on either side of the gap, 0.030 apart. Stock R also has the sample's lowest persistence, 0.654428, against Stock J's 0.998468. A horizon-averaged input remains untested; the paper names horizon-consistent multi-step or average-variance forecasts as future research. Stock A is maturity-led at a forecast of 0.379482 and still has significant residual ARCH (p = 0.027766).

The evidence for GJR asymmetry is thin, by the authors' account. Gamma is positive for twelve stocks, but significant at 5% only for Stock E and Stock P. GJR beats symmetric GARCH on AIC in 12 of 19. The authors use it as a flexible common model.

A cost index near zero

The 0.000225 cost index largely reflects the (1+tau) form and the 2% cap, which the authors acknowledge. Tau scales the price over [0, 0.02]. As they put it: "It is a scenario surcharge, not a structural claim about hedging costs."

Their reported mean first-order index for tau, 0.000285, exceeds its total-order index of 0.000225. The latter remains 0.000225 at N = 512, 1024 and 2048. For independent inputs, a total-order index cannot be smaller than its first-order counterpart. At this scale, the first-order estimate is noise. The wider domain yields 0.000368 and adds little.

We could not rerun this.

Our equity data focus on the US and lack Indonesian daily prices. Index X membership is masked in a confidential crosswalk, leaving us without a point-in-time constituent list to map.

The experiment would earn a trader's attention with a forecast variance term structure in place of fixed volatility and a check of simulated prices against quoted implied vols on these names. For now, the divide visible across Table 3 and Table 6 belongs to the Black-Scholes formula applied to 19 one-step-ahead forecasts from a single as-of date.