Surreal illustration of AI-driven financial calibration using neural networks and random data points.

Decoding Stochastic Volatility: How AI and Randomness Are Revolutionizing Financial Calibration

Jordan Keane in Business & Economy December 2025 • 4 min read.

"Discover the groundbreaking techniques that blend neural networks and random grids for superior financial model calibration and volatility prediction."

In the complex world of quantitative finance, accurately calibrating stochastic volatility models has long been a formidable challenge. These models are essential for pricing options and managing risk, but their effectiveness hinges on precise calibration—a process that aligns the model's output with observed market prices. Traditional methods often struggle with the computational intensity and the need for extensive interpolation and extrapolation, especially when dealing with sophisticated models like rough Bergomi and rough Heston.

Recent advancements in neural networks have opened new avenues for tackling these calibration challenges. Fabio Baschetti, Giacomo Bormetti, and Pietro Rossi introduce an innovative approach that marries the robustness of grid-based methods with the precision of pointwise calibration. Their technique leverages the power of neural networks to learn from randomly generated implied volatility surfaces, offering a pathway to more efficient and accurate model calibration.

This article delves into their methodology, exploring how it overcomes the limitations of traditional approaches and paves the way for valuable applications in financial engineering. From pricing under local stochastic volatility models to expanding the horizons of path-dependent volatility models, we'll uncover how these techniques are reshaping the landscape of financial modeling.

The Innovation: Neural Networks Meet Random Grids

Surreal illustration of AI-driven financial calibration using neural networks and random data points.

Baschetti, Bormetti, and Rossi's method represents a significant departure from conventional calibration techniques. It uniquely combines two prominent approaches: the grid approach pioneered by Horvath et al. (2021) and the pointwise two-stage calibration of Bayer et al. (2018) and Liu et al. (2019). The grid approach involves creating a structured framework across different strike prices and maturities, while the pointwise method focuses on calibrating individual data points without relying on interpolation.

The key innovation lies in generating implied volatility surfaces on random grids. These grids serve as the training data for the neural network, which learns to map model parameters to implied volatilities. By using random grids, the methodology avoids the pitfalls of interpolation and extrapolation, a common problem in traditional grid-based methods. This is particularly advantageous when dealing with models that lack closed-form solutions, such as rough volatility models.

Robustness: Inherits robustness from grid-based methods, ensuring stability in various market conditions.
Precision: Achieves high precision through pointwise calibration, capturing fine-grained details in volatility surfaces.
Efficiency: Reduces computational burden by eliminating the need for interpolation and extrapolation.
Versatility: Applicable to a wide range of stochastic volatility models, including rough Bergomi and rough Heston.

The neural network architecture is designed for efficiency, requiring only a small number of neurons to achieve accurate calibration. This is crucial for practical applications where speed and computational resources are paramount. The network takes model parameters, strike prices, and maturities as inputs and outputs the corresponding implied volatility, effectively learning the complex relationships that govern option prices.

The Future of Financial Calibration

The work of Baschetti, Bormetti, and Rossi signals a paradigm shift in financial calibration. By harnessing the power of neural networks and random grids, they have created a methodology that is not only more efficient and accurate but also more adaptable to the complexities of modern financial markets. As AI continues to advance, we can expect even more sophisticated techniques to emerge, further transforming the landscape of quantitative finance and risk management.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2306.11061,

Title: Deep Calibration With Random Grids

Subject: q-fin.pr q-fin.cp

Authors: Fabio Baschetti, Giacomo Bormetti, Pietro Rossi

Published: 19-06-2023

Everything You Need To Know

What is stochastic volatility and why is calibrating it so important in finance?

Stochastic volatility models are essential in quantitative finance for pricing options and managing financial risk. They account for the fluctuating nature of market volatility. Accurate calibration, the process of aligning model outputs with observed market prices, is critical because it ensures that the model correctly reflects market conditions. Precise calibration allows for accurate option pricing and effective risk management, which protects against potential financial losses. Without proper calibration, models can lead to incorrect valuations and poor risk assessments.

How does the approach by Baschetti, Bormetti, and Rossi improve the calibration of stochastic volatility models compared to traditional methods?

Baschetti, Bormetti, and Rossi introduce a novel approach by combining neural networks with random grids. Traditional methods often struggle with computational intensity and the need for interpolation and extrapolation, especially in complex models like rough Bergomi and rough Heston. The new method generates implied volatility surfaces on random grids, using these as training data for a neural network. This avoids the drawbacks of interpolation and extrapolation, common in grid-based methods, offering improved efficiency and accuracy. Their approach uniquely merges the grid approach (Horvath et al. (2021)) and pointwise two-stage calibration (Bayer et al. (2018) and Liu et al. (2019)).

What role do random grids play in the calibration methodology developed by Baschetti, Bormetti, and Rossi, and why are they important?

In the methodology, random grids serve as the foundation for training the neural network. Instead of using structured grids that can lead to interpolation and extrapolation errors, random grids provide a more flexible and robust way to sample the implied volatility surface. The neural network learns to map model parameters to implied volatilities based on data from these random grids. This avoids the limitations of traditional grid-based methods, particularly when dealing with complex models like rough Bergomi and rough Heston, which often lack closed-form solutions. This approach ensures robustness, precision, efficiency and versatility.

Can you explain the key benefits of using neural networks in calibrating stochastic volatility models?

Neural networks offer several advantages. They are designed for efficiency, requiring a small number of neurons to achieve accurate calibration, which is crucial for practical applications where speed and computational resources are limited. The network learns complex relationships by taking model parameters, strike prices, and maturities as inputs, and outputs the corresponding implied volatility. This allows the model to capture fine-grained details in volatility surfaces, leading to more precise calibration results. The method is also versatile, being applicable to a wide range of stochastic volatility models.

How might the techniques developed by Baschetti, Bormetti, and Rossi impact the future of financial modeling and risk management?

The techniques developed by Baschetti, Bormetti, and Rossi signal a paradigm shift in financial calibration by utilizing neural networks and random grids. This methodology offers improved efficiency, accuracy, and adaptability. As AI continues to advance, we can expect more sophisticated techniques to emerge. This will further transform quantitative finance, risk management, and potentially other areas like pricing under local stochastic volatility models and path-dependent volatility models. The ability to handle complex models and market conditions more effectively will be critical for financial institutions to make informed decisions.