A Simple Framework for the Stochastic Volatility Uncertainty

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. © 2025, University of Maragheh. All rights reserved.