Predicting Market Swings: A New Approach to Volatility Forecasting

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Author: Denis Avetisyan

Researchers are leveraging the power of diffusion models to more accurately predict implied volatility surfaces, offering improved risk management and option pricing capabilities.

The diffusion process reveals how implied volatility evolves, demonstrating its dynamic nature and inherent unpredictability.
The diffusion process reveals how implied volatility evolves, demonstrating its dynamic nature and inherent unpredictability.

This work introduces a conditional diffusion model for forecasting implied volatility surfaces, achieving higher accuracy and better-calibrated uncertainty estimates through a dynamically weighted arbitrage penalty.

Accurately forecasting implied volatility surfaces remains a challenge due to the inherent complexities of financial markets and limitations of existing generative models. This paper, ‘Forecasting implied volatility surface with generative diffusion models’, introduces a novel conditional diffusion model offering a stable and accurate alternative to GAN-based approaches for generating arbitrage-free implied volatility surfaces. By incorporating a dynamically weighted arbitrage penalty—guided by signal-to-noise ratio—the model steers generation toward realistic and financially sound outputs. Could this approach unlock more robust risk management and derivative pricing strategies in complex financial instruments?

Volatility’s Persistent Challenge

Accurate forecasting of the Implied Volatility Surface is critical for effective risk management and precise derivative pricing. This surface, representing implied volatility across strike prices and maturities, underpins options valuation and hedging. Miscalibration leads to financial losses and flawed portfolio management.

Traditional models, including parametric approaches like SABR or Heston, often struggle to capture the complexities of real-world volatility. They frequently rely on simplifying assumptions that limit predictive power, failing to account for phenomena like volatility skew and term structure variations.

The mean surface, calculated from log-implied volatilities within the training dataset, provides a comprehensive view of volatility distribution.
The mean surface, calculated from log-implied volatilities within the training dataset, provides a comprehensive view of volatility distribution.

Existing Generative Adversarial Networks (VolGAN) offer a data-driven approach, but lack the flexibility and robustness required for reliable forecasts across diverse market conditions. Improving generalization and stability remains a key challenge.

The shape of volatility reveals not just where we are, but all the paths not taken.

Diffusion Models for Volatility Forecasting

Denoising Diffusion Probabilistic Models (DDPMs) represent a significant advance in generative modeling, demonstrating efficacy in image synthesis and data imputation. These models progressively add noise to data, then learn to reverse the process to generate new samples.

This work leverages DDPMs to generate forecasts of the Implied Volatility Surface (IVS), addressing limitations in calibration and realistic representation of market dynamics. The implemented DDPM learns the underlying data distribution of the IVS, enabling more accurate and well-calibrated forecasts.

The diffusion model's architecture leverages a specific structure to generate and refine data distributions.
The diffusion model’s architecture leverages a specific structure to generate and refine data distributions.

At the core is a U-Net architecture, designed to efficiently predict noise at each diffusion step, enabling accurate estimation of the score function and generating high-fidelity IVS forecasts. The U-Net’s ability to capture both local and global features is critical.

Financial Validity and Accuracy

The developed Diffusion Probabilistic Model (DDPM) incorporates an $ArbitragePenalty$ within the $LossFunction$ to enforce the $NoArbitrageCondition$, preventing financially implausible forecasts. This directly addresses a key challenge in financial time series modeling – the need for economically coherent predictions.

The diffusion model exhibits a daily arbitrage penalty on the test set that closely aligns with the ground-truth penalty, as demonstrated by the comparison of the mean penalty (solid line) with the established benchmark (black line).
The diffusion model exhibits a daily arbitrage penalty on the test set that closely aligns with the ground-truth penalty, as demonstrated by the comparison of the mean penalty (solid line) with the established benchmark (black line).

To balance arbitrage prevention with forecast accuracy, the $ArbitragePenalty$ is dynamically weighted using $SNRWeighting$. An Exponential Moving Average (EMA) is employed to smooth the U-Net parameters during training, enhancing stability and convergence. Rigorous evaluation demonstrates a lower $MeanAbsolutePercentageError$ of 3.0026% compared to the $VolGAN$ benchmark of 3.7304%, indicating improved accuracy and economic coherence.

Calibration and Theoretical Guarantees

A central contribution of this work is a novel forecasting model demonstrating improved calibration of predicted confidence intervals. Calibration is assessed by measuring how often true values fall outside the predicted intervals; the model achieves well-calibrated 90% confidence intervals with a breach rate near the theoretical 10% target, a significant advancement over existing methods.

Training and validation loss curves indicate the model's learning progress and generalization capability.
Training and validation loss curves indicate the model’s learning progress and generalization capability.

The model’s stability and reliability are ensured through a carefully designed training process. The incorporation of the ArbitragePenalty, coupled with a specifically chosen LossFunction, leads to a ConvergenceGuarantee. Furthermore, the model supports ConditionalGeneration, enabling the production of forecasts tailored to specific market conditions, enhancing its practical utility.

The ability to generate nuanced predictions based on contextual factors distinguishes this work. By incorporating conditional inputs, the model moves beyond simple point forecasts, offering a more comprehensive view of potential future outcomes. Such granularity is invaluable for informed decision-making, suggesting that the true measure of prediction isn’t simply seeing the future, but understanding the shape of its possibilities.

The research demonstrates a commitment to parsimony in modeling the implied volatility surface, a complex financial construct. The generative diffusion model, by focusing on stable training and a dynamically weighted arbitrage penalty, effectively reduces unnecessary complexity. This aligns with a preference for extracting maximum signal with minimal parameters. As Paul Feyerabend stated, “Anything goes.” – a sentiment resonating with the exploration of novel approaches, even those diverging from established norms, to achieve a more accurate and calibrated forecast. The study’s success highlights how embracing methodological pluralism, rather than rigidly adhering to pre-defined constraints, can yield superior results in forecasting financial derivatives.

Where to Next?

The pursuit of a generative model for implied volatility surfaces, as demonstrated, sidesteps the direct estimation of complex stochastic processes. This is a virtue, not a failing. However, the current architecture, while outperforming alternatives, remains tethered to the observable surface itself. Future iterations should interrogate the underlying, latent dimensions driving volatility dynamics, not merely replicate the visible manifestation. The arbitrage penalty, a necessary corrective, hints at a deeper truth: the model learns a constraint, not a principle.

A natural extension lies in extending this framework beyond a single surface. Volatility surfaces evolve. A truly generative model would not predict a static image, but a dynamic process, incorporating temporal dependencies without reverting to the rigidity of parametric time series models. The challenge isn’t simply to predict the surface at a future date, but to generate a plausible path of surfaces, acknowledging inherent uncertainty without obscuring it with overconfident point estimates.

Ultimately, the value of this work resides not in achieving incremental gains in forecast accuracy—those gains are fleeting—but in shifting the question. The goal is not to ‘solve’ volatility, a task bordering on the absurd, but to create a minimal, elegant framework for representing its inherent ambiguity. Simplicity, after all, is the ultimate refinement.

Original article: https://arxiv.org/pdf/2511.07571.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2025-11-13 02:27