What question did this study set out to answer?

The central aim is to establish a framework for analyzing uncertainty in stochastic volatility processes.

February 25, 2026SHILAP Revista de lepidopterología0 citationsOpen Access

A Simple Framework for the Stochastic Volatility Uncertainty

Key Points

The central aim is to establish a framework for analyzing uncertainty in stochastic volatility processes.
Developed an uncertainty framework using a Cox-Ingersoll-Ross process to model volatility bounds.
Analyzed worst-case and best-case scenario prices for contingent claims.
Computed prices using data from the parameterized Heston model.
Illustrated findings with numerical examples.
Demonstrated that worst-case and best-case prices can be simplified based on convex or concave payoff functions.
Concluded that scenarios align with parameterized Heston model outputs under specific conditions.

Abstract

This paper presents an uncertainty framework, in which the volatility process exists within a random interval defined by bounds modeled by a Cox-Ingersoll-Ross (CIR) process. We analyzed the worst-case and best-case scenario prices of a simple contingent claim within this framework, demonstrating that it can be computed using prices from the parameterized Heston model. We also proved that if the payoff function is convex (concave), the worst-case and best-case scenario prices simplify to the price derived from the parametrized Heston model with specified parameters. Finally, we concluded with numerical examples to illustrate our findings.

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