A listed put needs a better reason for a new quote than the delta result Teng reports here. His solver is quick and fairly accurate for American puts under stochastic local volatility with random spot-vol correlation. At 400 time steps, it resolves a SABSR price effect of 1.9% to 3.8% of premium at K = 1.00. The delta effect is 0.041 to 0.047, close to the 0.035 drift in constant-correlation delta as the grid is refined. That drift has not visibly stopped. The paper has yet to justify quoting a listed put differently.
Where would the trading edge come from?
Teng starts with a stochastic local volatility (SLV) model: spot diffuses as α(ν)β(S)dW, and the volatility factor ν has its own SDE. Instead of holding the correlation between spot and vol shocks constant, he lets ρ_t move. In the main experiments it follows the bounded correlation process of Teng et al. (2016a), dρ = κ(μ−ρ)(1−ρ²)dt + σ(1−ρ²)dW, and stays inside (−1, 1). Teng names the family SCLV, for stochastic correlation local volatility. Its tested members are SABSR, SABR with stochastic rho, and HSCLV, Heston SLV with stochastic rho. The trading case rests on correlation risk: if spot-vol correlation moves and the market prices that movement, a constant-ρ model gets both put value and hedge wrong.
The solver prices the put through a reflected backward SDE. An increasing process pushes option value Y up whenever it would cross below the exercise payoff; martingale term Z carries the hedge ratios. The scheme works backward through N_T dates, estimating Z from E[Y·ΔW]/Δt at each one. It then uses 10 Picard iterations for the implicit continuation value before taking the max with intrinsic value. XGBoost supplies every conditional expectation, with depth 2, learning rate 0.9, up to 150 trees, early stopping after 1 round, and a 3:1 train/test split. Figures average 10 seeded runs using 100,000 paths (SABR) or 200,000 (Heston). All paths are simulated. The paper uses no market data or calibration.
For constant-correlation prices, Teng compares against CTMC, the Markov-chain method of Cui et al. For stochastic correlation, the comparator is DPDB, the deep primal-dual BSDE method of Yang and Li; it reports lower and upper price bounds with confidence intervals.
The price effect is small enough to check carefully
At S0 = 1.1 and K = 1.00, the constant-ρ SABR put with ρ = −0.4 prices at 0.0403 for N_T = 100, 0.0413 for 200, and 0.0425 for 400. CTMC gives 0.0424. Teng calls N_T = 100 "comparable" to CTMC, though its price is 5% below that benchmark. The close match comes at 400 steps. At K = 1.20, the N_T = 100 miss is 1.8% of premium, with 0.1435 against 0.1461; the solver reaches 0.1464 at 400 steps.
With stochastic correlation switched on, ρ0 = μρ = −0.4 and σρ = 0.5. At N_T = 400 and K = 1.00, prices are 0.0440 for κρ = 0.1, 0.0441 for 2.0, and 0.0433 for 20. Relative to the constant-ρ price of 0.0425, the shift is about 1.9% to 3.8% of premium. The N_T = 100 grid bias, 0.0425 minus 0.0403, exceeds each shift, though the shifts themselves are measured at N_T = 400. At that grid size, the constant-ρ price misses CTMC by only 0.0001 at K = 1.00 and 0.0003 at K = 1.20. Run standard deviations are near 3.5E-04. A shift of 0.0008 to 0.0016 is therefore measurable on this grid.
HSCLV moves less. Changing its long-run correlation mean from −0.2 to 0.75 takes the at-the-money Heston put from 0.2794 to 0.2755, about 1.4%. Deep in-the-money strikes yield 0.9999, 1.9999 and 2.9999 with zero run variance. Teng says the impact of stochastic correlation "almost disappears" at those strikes, then writes: "We may conclude that stochastic correlation plays a minor role when other parameters have dominant values in determining the option value." His conclusion also claims a "significant impact of stochastic correlation on both pricing and delta-hedging". The strikes nearer the money must carry that claim: 1.9% to 3.8% of premium in SABSR, 1.4% in HSCLV, and a delta shift comparable to grid drift that has yet to converge.
Delta has a grid problem
The price evidence is stronger than the hedge evidence. At K = 1.00 under constant correlation, delta goes from −0.2564 to −0.2376 to −0.2214 as N_T rises from 100 to 400. The price converges over the same grids.
No benchmark delta is reported.
At the same N_T and M, SABSR gives deltas of −0.2681, −0.2687 and −0.2624 for κρ = 0.1, 2 and 20. They are 0.041 to 0.047 more negative than the constant-ρ result of −0.2214. Grid refinement from N_T = 100 to 400 moved that constant-ρ result by 0.035. At κρ = 20, correlation reverts to −0.4 almost instantly. Teng says those approximations "are expected to closely resemble those obtained with the constant correlation value"; a 0.041 gap remains. The K = 1.00 run std of 1.50E-02 to 1.57E-02 is roughly a third of the gap, which makes noise an insufficient explanation. Bias remains possible. Constant-ρ delta still changed by 0.016 between N_T = 200 and 400, and without a benchmark delta we cannot separate bias from effect.
Teng is candid about the other Greeks. He drops vol and correlation sensitivities because extracting them from Z requires ill-conditioned systems: "As a result, we limit our discussion only to delta-hedgings in this paper." That disclosure is to his credit. The correlation hedge that motivates the model remains unavailable.
A disagreement between the solvers
Teng says his prices "fall within the corresponding confidence intervals" from DPDB. At κρ = 0.1 and K = 1.00, that interval runs from [0.0418, 0.0485], about 0.0067 wide. It contains the constant-correlation price of 0.0425, as does the κρ = 2 interval [0.0421, 0.0461]. These checks cannot distinguish the stochastic-correlation model from its constant-ρ parent.
The point estimates raise a sharper issue. At K = 1.00, DPDB gives 0.0419 for κρ = 0.1, 0.0422 for κρ = 2, and 0.0419 for κρ = 20. Each falls below the constant-ρ CTMC price of 0.0424. Teng's RBSDE solver instead puts stochastic-correlation prices above it, from 0.0433 to 0.0441. At this strike, the solvers disagree on the direction of the correlation effect. Their 0.0021 gap at κρ = 0.1 is larger than the effect being measured. Teng's speed advantage is clear: about 210 s per run against 637 s of DPDB training on SABSR, and 35 s against 639 s on HSCLV. The prices in the tables average ten runs.
There are limits beyond the solver comparison. Both stochastic-correlation experiments set ρρν = 0, leaving the permitted coupling of correlation and vol noise untested. We did not find the values of risk premia λρ and λν used in the runs; the paper notes that those premia are not unique. Its convergence theorem assumes globally Lipschitz coefficients, an assumption the νS^β and √ν diffusions used here do not meet.
What would change the trading case?
A premium shift of 1.4% (HSCLV, μρ from −0.2 to 0.75) to 3.8% (SABSR, κρ = 2) matters only if listed American puts depart from calibrated SCLV values by that amount in a stable direction. A market check would calibrate SABSR and its constant-ρ parent daily on US single-name and ETF puts, rank contracts by market price minus model value, then delta-hedge with shares out of sample after quoted spreads and rebalancing costs. The SCLV ranking would need to beat the constant-ρ ranking after costs. Its 0.041 to 0.047 delta gap would also need to reduce hedging error.
Until then, Teng has a credible fast solver and a price effect of 1.9% to 3.8% of premium that it resolves at 400 steps. The delta effect remains unresolved.