Pauquay's rough Bergomi pricer deserves a desk's attention: it matches same-model simulations to 0.9 to 2.2bp of implied vol and prices forward-start smiles and barriers from the same field. Those are numerical accuracy figures inside the model. They say nothing about distance to a market quote. The paper's multi-asset example uses FX; we have no FX data. Our screen instead uses US equity and ETF options, hedged with the underlying shares and ETFs. The rough Bergomi pricer and response-kernel Greeks look useful. Whether they identify a wrong quote remains open.

The engine Pauquay built

A stochastic-volatility price is the expectation of a nonlinear function of a Gaussian field. The noise is Gaussian in log-volatility coordinates; the smile arises from what is done to it, whether variance is the exponential of a latent factor or SABR applies a CEV power. Pauquay takes the two-particle-irreducible effective action from field theory and approximates the joint law of the state variables with a Gaussian whose covariance solves a self-consistency condition. He calls the result the Self-Consistent Gaussian (SCG) closure. Its useful trick is to evaluate an exponential vertex with the exact Gaussian moment-generating function. Cutting off its Taylor series would lose terms that matter at long maturity and high vol-of-vol.

The computational split comes from the dressed inverse propagator. When it is local in time, as in exp-OU and SABR, a few ODEs suffice. Exp-OU takes three per smile and produces 0.1 to 0.2bp RMSE at ρ=0. Rough Bergomi and rough SABR have a nonlocal propagator, so the engine retains the full two-time Volterra covariance. Conditional on a volatility path, the log-return is Gaussian or exact-CEV. PCA-ordered Sobol randomised quasi-Monte Carlo (RQMC) then integrates across paths. That covariance also prices forward-start smiles and barriers, while the causal response kernel supplies bucketed vega. The paper uses no market data. Its references are Sobol runs of 2^18 to 2^20 paths, PDEs and the rough Heston transform, each applied to the same model.

Which pricer belongs on an end-of-day screen?

Rough Bergomi's conditional-path engine is the candidate. Its Level-1 SCG closure misses implied vol by 186, 405 and 733bp across the mild, moderate and extreme regimes. The conditional-path RQMC, by contrast, reaches 0.9, 1.5 and 2.2bp at 32k nodes on K/F between 0.85 and 1.15, measured against a 2^19-path reference. In the strong-coupling cell at one year, a deep-wing residual of tens of bp in vol amounts to 0.18bp of spot because vega collapses. Pauquay credits conditional Monte Carlo for rough Bergomi as established technology that his framework organises rather than originates. He also warns that the ± bars omit noise in the reference itself. The reported agreement therefore reaches a noise floor. Both qualifications matter.

For a screen, the wider strikes give a sterner measure. Across the full strike range, the arbitrage-free conditional-Black average stays within about 14bp of Monte Carlo. The gap is a few bp near the money and widens in the deep wings.

Rough SABR is too loose for this use. Its mean RMSE over the test grid is about 17bp, with a max of about 68bp; a separate equity-skew slice misses one deep low-strike strike at the longest maturity by 72bp. SABR with boundary-proximity routing sends difficult cells to a lattice solver and averages 7.4bp over 72 cells, though its worst cell reaches 53.2bp. At five years, Hagan's error spans 28 to 57bp across the grid. In the paper's Figure 4 panel, DS stays within 0.6 to 8.7bp and Hagan reaches 51 to 72bp.

Simulation accuracy and market prices

Pauquay describes every accuracy result as coming "from controlled model-to-model validation against a synthetic benchmark of the same model." His reason is sound for a numerical study: a parsimonious model has fewer parameters than a smile has quotes, and a market residual would mix model misspecification with pricing error. The resulting evidence establishes how closely the engine prices its own model. The paper deliberately leaves aside the market-fit question that matters to a trading desk.

Its multi-asset example is an FX triangle fitted to a synthetic EUR/JPY target. The full fit reduces the cross residual from 5.8bp to 0.2bp for exp-OU and from 9.3bp to 1.5bp for rough. Recovering couplings from a synthetic target checks self-consistency. We have no FX data, so our rough Bergomi screen uses US equity and ETF options and hedges with the underlying shares and ETFs. The paper benchmarks the engine at equity-style correlations (ρ=-0.7), against its own simulations only. Our walk-forward screen works as follows:

Results are not in yet.

The Greeks deserve the next test

The response contraction matches bump-and-revalue impulse vega at an RMSE of about 10^-12. Its cost is roughly 70 times lower for the OU kernel and 80 times lower for the fractional one, with the ratio growing linearly as bucket count rises. Pauquay is clear about the limits: 10^-12 is agreement between derivative implementations, and the buckets measure sensitivity to latent factors. Quote-space vega requires a calibration Jacobian, which he leaves for future work.

Speed comparisons also depend on the contract. For a single exp-OU one-touch, a 2-D PDE takes 6.6s with +4.6bp error; the best conditional-Gaussian variant takes 9.1s with +0.7bp error. Both fall inside the ±9.7bp Monte Carlo band. Pauquay calls the PDE the fastest route for a single contract. In rough Bergomi, the one-touch is only 1.7 times faster than simulation, whereas smooth forward-vol agreement is 14 times faster. The timings are from single-thread Python, and the paper calls them indicative.

A hedging experiment would change my view. Calibrate to quotes, carry the response buckets through that Jacobian, then compare delta-vega hedged P&L variance with quote-space bumps. If the buckets reduce hedging error after costs, the 80-times speed-up has trading value. Until then, this remains a fast, carefully validated pricer for a model whose relation to market quotes the paper has not tested.