Surreal illustration of volatility in financial markets.

Decoding Volatility: How the Sandwiched Volterra Model is Shaking Up Option Pricing

Mira Elwood in Business & Economy December 2025 • 4 min read.

"Explore the innovative Sandwiched Volterra Volatility (SVV) model and how it's addressing critical limitations in traditional financial modeling to offer more accurate option pricing."

For decades, the Black-Scholes model has been a cornerstone of financial mathematics, providing a relatively simple framework for option pricing. However, real-world financial markets are far more complex than this model accounts for. One of the most glaring issues is the assumption of constant volatility, a measure of how much a stock price fluctuates. In reality, volatility is anything but constant.

Volatility often exhibits clustering, meaning periods of high volatility are followed by more high volatility, and vice versa. There's also a well-documented inverse relationship between asset prices and volatility; as stock prices fall, volatility tends to rise, and when prices rise, volatility decreases. Most visibly, the implied volatility surface, which plots option prices across different strike prices and maturities, displays a pronounced “smile” or “skew,” a clear deviation from the flat surface predicted by the Black-Scholes model.

To address these shortcomings, financial engineers have developed a range of stochastic volatility models, where volatility itself is treated as a random variable. These models can capture some of the dynamic features missed by Black-Scholes, but they often come with their own set of challenges. A recent paper introduces a novel approach: the Sandwiched Volterra Volatility (SVV) model. This model attempts to reconcile the need for both realism and mathematical tractability by carefully constraining the behavior of volatility within predefined boundaries.

What Makes the Sandwiched Volterra Volatility (SVV) Model Unique?

Surreal illustration of volatility in financial markets.

The Sandwiched Volterra Volatility (SVV) model introduces a few key innovations to tackle long-standing issues in financial modeling:

Unlike models relying on standard Brownian motion, the SVV model uses a more general Gaussian Volterra process to drive volatility. This allows the model to capture both the "roughness" observed in short-term volatility and the long memory effects seen over longer periods. This flexibility is crucial for accurately pricing options across different maturities.

Sandwiched Volatility: The model ensures that volatility remains within a specific range defined by two arbitrary functions. This "sandwiching" effect helps to keep the model stable and prevents unrealistic volatility spikes.
Arbitrage-Free Pricing: The SVV model provides a clear way to define equivalent martingale measures, which are essential for risk-neutral pricing and avoiding arbitrage opportunities.
Malliavin Calculus: The model leverages Malliavin calculus, a powerful tool for analyzing the sensitivity of option prices to changes in underlying parameters, especially useful for options with discontinuous payoffs.

However, rough volatility models are also not perfect. They tend to exhibit the following issues:

The Future of Option Pricing?

The Sandwiched Volterra Volatility model represents a significant step forward in financial modeling. By addressing key limitations of existing approaches and incorporating more realistic features of volatility, it provides a more robust and flexible framework for option pricing. While still a relatively new model, its potential impact on risk management and investment strategies could be substantial.

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This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2209.10688,

Title: Option Pricing In Sandwiched Volterra Volatility Model

Subject: q-fin.mf math.pr

Authors: Giulia Di Nunno, Yuliya Mishura, Anton Yurchenko-Tytarenko

Published: 21-09-2022

Everything You Need To Know

What are the primary limitations of the Black-Scholes model that the Sandwiched Volterra Volatility (SVV) model aims to address?

The Black-Scholes model assumes constant volatility, which doesn't reflect real-world market dynamics. Volatility exhibits clustering, where high volatility periods follow high volatility periods, and vice versa. There's also an inverse relationship between asset prices and volatility. The implied volatility surface deviates from the flat surface predicted by Black-Scholes, displaying a "smile" or "skew." The Sandwiched Volterra Volatility (SVV) model addresses these by allowing volatility to be dynamic and by incorporating features like "roughness" and long memory effects using a Gaussian Volterra process.

How does the Sandwiched Volterra Volatility (SVV) model ensure stability and prevent unrealistic volatility spikes?

The Sandwiched Volterra Volatility (SVV) model uses a "sandwiching" effect, ensuring that volatility remains within a specific range defined by two arbitrary functions. By constraining volatility within these predefined boundaries, the model maintains stability and prevents extreme, unrealistic spikes in volatility. This is one of the key innovations of the Sandwiched Volterra Volatility (SVV) model to create more realistic option pricing strategies.

What role does Malliavin calculus play in the Sandwiched Volterra Volterra Volatility (SVV) model, and why is it important?

Malliavin calculus is used in the Sandwiched Volterra Volatility (SVV) model to analyze the sensitivity of option prices to changes in underlying parameters. It is particularly useful for options with discontinuous payoffs. By leveraging Malliavin calculus, the model enhances its ability to manage risk effectively, particularly for complex option strategies.

In what ways does the Sandwiched Volterra Volatility (SVV) model improve upon traditional stochastic volatility models?

Traditional stochastic volatility models, while addressing the constant volatility issue of Black-Scholes, often come with their own challenges. The Sandwiched Volterra Volatility (SVV) model introduces innovations such as using a Gaussian Volterra process to capture both "roughness" in short-term volatility and long memory effects seen over longer periods. It also ensures volatility remains within specific boundaries, preventing unrealistic volatility spikes, and offers a clear way to define equivalent martingale measures for risk-neutral pricing, which improves accuracy and market adaptability compared to the traditional models.

What are the potential implications of the Sandwiched Volterra Volatility (SVV) model for risk management and investment strategies?

The Sandwiched Volterra Volatility (SVV) model represents a significant advancement in financial modeling, offering a more robust and flexible framework for option pricing by addressing key limitations of existing approaches and incorporating more realistic features of volatility. Its potential impact on risk management and investment strategies could be substantial, providing more accurate pricing and hedging strategies. However, further research and testing are needed to fully understand its implications and limitations. Moreover, while the Sandwiched Volterra Volatility (SVV) model addresses issues of roughness, further exploration is needed on how to resolve the issues presented by these models.