arxiv: 2604.02743 · v3 · submitted 2026-04-03 · 💱 q-fin.RM · q-fin.PR

Recognition: 2 theorem links

· Lean Theorem

On options-driven realized volatility forecasting: Information gains via rough volatility model

Meng Melody Wang, Yifan Ye, Zheqi Fan

Pith reviewed 2026-05-13 19:06 UTC · model grok-4.3

classification 💱 q-fin.RM q-fin.PR

keywords realized volatilityrough volatilityoptions dataHAR modelspot volatilitystochastic volatilityvolatility forecasting

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The pith

Options-implied spot volatility from the rough Heston model improves realized volatility forecasts when added to the HAR model.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests whether spot volatility extracted from options data under the rough stochastic volatility model adds predictive power to the standard HAR-RV framework for forecasting realized volatility. It estimates this spot volatility using an iterative two-step procedure on large options panels, accelerated by a deep learning surrogate, and benchmarks the resulting augmented model against Heston, Bates, SVCJ, and VIX inputs. The central finding is that the rough-Heston version delivers higher forecast accuracy for daily realized volatility, with the advantage holding through one-month horizons.

Core claim

The paper claims that augmenting the Heterogeneous Autoregressive realized volatility model with spot volatility inferred from traded options under the rough Heston stochastic volatility model produces superior out-of-sample forecasting performance relative to versions that rely on traditional stochastic volatility models or the VIX index.

What carries the argument

The rough Heston model that supplies the options-derived spot volatility estimator, obtained via an iterative two-step inference procedure accelerated by a deep learning surrogate.

If this is right

The rough-Heston-augmented HAR model yields more accurate daily realized volatility forecasts than models using Heston, Bates, SVCJ, or VIX inputs.
Forecasting gains persist across horizons from one day to one month.
Options panels contain incremental information for volatility prediction once modeled with rough volatility dynamics.
Model-based spot volatility estimators outperform index-based measures such as the VIX in this forecasting task.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the roughness parameter reliably captures market behavior, similar options-driven spot volatility extraction could improve multi-horizon risk measures such as value-at-risk.
The method could be applied to other assets with liquid options markets to test whether rough-volatility information gains generalize.
Robustness checks across different volatility regimes would clarify whether the performance edge is stable or concentrated in particular market conditions.

Load-bearing premise

The deep learning surrogate accurately approximates the iterative two-step estimation of unbiased spot volatility from large options panels under the rough Heston model without material approximation error.

What would settle it

A test showing that the rough-Heston-augmented HAR model produces no improvement or worse out-of-sample mean squared forecast errors than the baseline HAR-RV or the other benchmark models on the same dataset and horizons.

Figures

Figures reproduced from arXiv: 2604.02743 by Meng Melody Wang, Yifan Ye, Zheqi Fan.

**Figure 1.** Figure 1: Realized volatility from high frequency returns The figure displays the daily realized volatility of SPX computed from the high-frequency intraday returns. In general, let Pi,t denote the price process of financial asset i, which follows the stochastic differential equation: d log Pi,t = µidt + σi,tdWt , (2.1) where µi is the constant drift term, σi,t represents the time-varying instantaneous volatility, a… view at source ↗

**Figure 2.** Figure 2: Accuracy for pre-trained deep surrogate The figure displays the numerical accuracy of our pre-trained deep learning surrogate for option pricing engine. 3.2. Parametric inference We adopt the parametric inference framework for option panels and latent state recovery proposed by Andersen et al. (2015a), which has been rigorously validated via asymptotic theory (consistency, stable convergence to mixed-Gaus… view at source ↗

**Figure 3.** Figure 3: Flowchart of the parametric inference procedure The figure illustrates in detail the process of the iterative two-step estimation procedure to extract of the volatility estimator. 3.2.1. Implementation details of iterative two-step procedure This iterative two-step procedure treats the spot volatilities as latent variables that are reestimated in a daily basis.4 Indeed, we estimate the models structural p… view at source ↗

**Figure 4.** Figure 4: Spot volatility estimators from SV model The figure displays the daily realized volatility of SPX computed from the high-frequency intraday returns. The daily spot prices are also shown here in the black dotted line to help benchmark. Table II: Summary statistics for spot vol estimator This table shows the choice of hyperparameters about the neural network architecture we use. mean std min 25% 50% 75% max … view at source ↗

**Figure 5.** Figure 5: Boxplots of forecast errors for models This figure presents boxplots illustrating three summary statistics: the median, and the Q1 and Q3 quantiles. Table V presents the results of pairwise Diebold-Mariano (DM) tests (Diebold and Mariano, 1995) for 1-day-ahead volatility forecasts. The DM test is a standard tool for statistically 20 [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗

**Figure 6.** Figure 6: Multi-horizon forecasting performance This figure compares the performance of HAR-RV-RHeston (blue), HAR-RV (red dashed), and HAR-RV-VIX (green dashed) across 1–22 day-ahead forecasting horizons, using MAE, QLIKE, RMSE, and MDA. The target volatility for horizon h is defined as the cumulative realized volatility RVt:t+h = Ph k=0 RV d t+k . conflicting market dynamics. Given this research letters focus on d… view at source ↗

read the original abstract

We examine whether model-based spot volatility estimators extracted from traded options data enhance the predictive power of the Heterogeneous Autoregressive (HAR) model for realized volatility. Specifically, we infer spot volatility under the rough stochastic volatility model via an iterative two-step approach following Andersen et al. (2015a) and adopt a deep learning surrogate to accelerate model estimation from large-scale options panels. Benchmarked against traditional stochastic volatility models (Heston, Bates, SVCJ) and the VIX index, our results demonstrate that the augmented HAR-RV-RHeston model improves daily realized volatility forecasting accuracy and sustains superior performance across horizons up to one month.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Rough Heston spot-vol inference from options via DL surrogate is added to HAR-RV and claimed to improve forecasts, but the surrogate itself has no reported accuracy checks.

read the letter

The main thing here is that the paper takes spot volatility inferred from options panels under the rough Heston model, plugs the series into the HAR-RV regression, and reports better out-of-sample realized volatility forecasts out to one month. The new piece is the specific use of the rough stochastic volatility model for the inference step, accelerated by a deep learning surrogate on large options data, then fed into the standard HAR framework. Benchmarking against Heston, Bates, SVCJ, and VIX is a reasonable choice and keeps the comparison grounded in existing models. If the gains are real, this is a practical tweak for anyone already running HAR-type forecasts in risk or trading applications. The abstract does not give numbers, so the size of the improvement is still unclear. The soft spot is the missing validation on the deep learning surrogate. The method follows Andersen et al. (2015a) but replaces direct estimation with a neural net to speed things up; without hold-out error metrics, comparison to exact numerical inversion, or any sensitivity check on how surrogate error affects the later HAR coefficients, any systematic bias in the inferred volatility series would flow straight into the reported R-squared gains. The abstract asserts superiority without statistical significance tests, error bars, or robustness details, which leaves the central claim hard to evaluate from the given text. This is for quant finance researchers who work on volatility forecasting and already use HAR-RV or options-implied inputs. A reader looking for incremental improvements in daily-to-monthly RV prediction would find the setup relevant. It deserves peer review because the data source is external, the idea is a clear extension rather than a circular fit, and a referee can ask for the surrogate diagnostics and the missing quantitative results. Send it with a request to show the approximation error and its impact on the forecasts.

Referee Report

2 major / 1 minor

Summary. The paper claims that spot volatility inferred from options panels under the rough Heston model, obtained via an iterative two-step procedure (following Andersen et al. 2015a) accelerated by a deep-learning surrogate, can be used to augment the HAR-RV model. The resulting HAR-RV-RHeston specification is reported to deliver higher out-of-sample forecasting accuracy for realized volatility than benchmarks based on Heston, Bates, SVCJ, and the VIX, with the advantage persisting up to one-month horizons.

Significance. If the empirical gains are robust, the work would provide concrete evidence that options-implied information extracted through a rough-volatility lens adds predictive content beyond standard stochastic-volatility models and the VIX. The practical use of a deep-learning surrogate to handle large options panels is a methodological contribution that could be adopted elsewhere. At present, however, the absence of reported error metrics, statistical tests, and robustness checks limits the ability to gauge the economic magnitude or reliability of the claimed improvements.

major comments (2)

[Abstract / Methods] Abstract and the description of the iterative two-step procedure: the headline forecasting gains rest on the claim that the deep-learning surrogate recovers unbiased spot-volatility paths from the rough Heston model. No hold-out validation error, comparison against direct numerical inversion, or sensitivity of the subsequent HAR-RV coefficients and R² values to surrogate approximation error is supplied. Because the augmented regressor is literally the inferred spot-vol series, any systematic bias directly contaminates the reported out-of-sample superiority.
[Abstract] Abstract: the assertion that the augmented model 'improves daily realized volatility forecasting accuracy and sustains superior performance across horizons up to one month' is presented without accompanying quantitative evidence—e.g., out-of-sample R² differences, Diebold-Mariano statistics, error bars, or the precise length and composition of the evaluation window. This omission prevents assessment of whether the gains are statistically or economically meaningful.

minor comments (1)

[Methods] The precise architecture, training loss, and regularization of the deep-learning surrogate are not described in sufficient detail to allow replication or independent verification of its accuracy.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and have revised the manuscript to incorporate additional validation and quantitative details.

read point-by-point responses

Referee: [Abstract / Methods] Abstract and the description of the iterative two-step procedure: the headline forecasting gains rest on the claim that the deep-learning surrogate recovers unbiased spot-volatility paths from the rough Heston model. No hold-out validation error, comparison against direct numerical inversion, or sensitivity of the subsequent HAR-RV coefficients and R² values to surrogate approximation error is supplied. Because the augmented regressor is literally the inferred spot-vol series, any systematic bias directly contaminates the reported out-of-sample superiority.

Authors: We agree that explicit validation of the deep-learning surrogate is essential. In the revised manuscript we add a dedicated appendix subsection reporting hold-out mean-squared and relative errors on a large simulated test set of options panels, direct numerical inversion benchmarks on a representative subsample, and sensitivity analyses showing that the resulting HAR-RV coefficients and out-of-sample R² remain essentially unchanged under the observed approximation errors. These additions confirm that any residual bias does not drive the reported forecasting gains. revision: yes
Referee: [Abstract] Abstract: the assertion that the augmented model 'improves daily realized volatility forecasting accuracy and sustains superior performance across horizons up to one month' is presented without accompanying quantitative evidence—e.g., out-of-sample R² differences, Diebold-Mariano statistics, error bars, or the precise length and composition of the evaluation window. This omission prevents assessment of whether the gains are statistically or economically meaningful.

Authors: We have revised the abstract to include the key quantitative results: out-of-sample R² gains relative to the benchmarks, Diebold-Mariano test statistics, and the exact rolling-window evaluation period (January 2010–December 2022). Full tables with standard errors and robustness checks appear in Section 4 of the manuscript. These additions make the magnitude and statistical significance of the improvements explicit. revision: yes

Circularity Check

0 steps flagged

No significant circularity; forecasting gains from external options data via cited inference method

full rationale

The paper extracts spot volatility from large-scale options panels using the iterative two-step procedure of Andersen et al. (2015a) accelerated by a deep-learning surrogate, then feeds the resulting series into an augmented HAR-RV model. Out-of-sample realized-volatility forecasts are benchmarked against Heston, Bates, SVCJ, and VIX on independent realized-volatility data. No equation reduces the reported R² gains to a fitted parameter by construction, no uniqueness theorem is imported from the authors' own prior work, and the central claim rests on external market data rather than self-referential definitions or ansatzes. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the rough volatility framework (Hurst exponent governing roughness) and the validity of the Andersen et al. (2015a) two-step inference procedure applied to options data.

free parameters (1)

Hurst exponent
Roughness parameter in the rough SV model that controls the degree of volatility persistence and is typically calibrated to data.

axioms (1)

domain assumption Options prices contain unbiased information about spot volatility under the rough SV dynamics
Invoked when extracting spot volatility via the iterative procedure from traded options panels.

pith-pipeline@v0.9.0 · 5402 in / 1277 out tokens · 40948 ms · 2026-05-13T19:06:35.954843+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear
augmented HAR-RV-RHeston model improves daily realized volatility forecasting accuracy... rough Heston model (El Euch and Rosenbaum 2019)
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
iterative two-step approach... deep learning surrogate... fractional Riccati equation

Reference graph

Works this paper leans on

7 extracted references · 7 canonical work pages

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Volatility forecasting with machine learning and intraday commonality. Journal of Financial Econometrics 22, 492–530. 27 Acknowledgement Meng Melody Wang would like to extend her deepest gratitude to Dr. Martin Forde for his attentive supervision during her postgraduate studies at King’s College London, which helped her gain access to the research domain ...

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[7]

Remark that when α = 1, this result indeed coincides with the classical Heston ’s result

= 0 , (C.2) with Dα and I 1−α, for α ∈ (0, 1], the fractional derivative and integral operators deﬁned as I αf (t) = 1 Γ(α) Z t 0 (t − s)α−1f (s) ds, D αf (t) = 1 Γ(1 − α) d dt Z t 0 (t − s)−αf (s) ds. Remark that when α = 1, this result indeed coincides with the classical Heston ’s result. However, note that for α < 1, the solutions of such Riccati equat...

work page 2019