TITLE:
A Trapezoidal Fuzzy Heston Model Calibrated to Copper Futures Prices
AUTHORS:
Kankolongo Kadilu Patient, Kumwimba Seya Didier, Panga Lutanda Grégoire, Balowayi Bondu Bernard, Mwania Wakosia José
KEYWORDS:
Heston Model, Trapezoidal Fuzzy Numbers, -Cuts, Fuzzy Stochastic Volatility, Copper Futures, Fuzzy Deep Galerkin Method, Fuzzy Calibration, Uncertainty Quantification, Commodity Derivatives
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.16 No.2,
June
11,
2026
ABSTRACT: This paper develops a fuzzy stochastic volatility framework for pricing and calibrating copper futures contracts under parameter uncertainty. The classical Heston model is extended by representing its structural parameters as trapezoidal fuzzy numbers, allowing the model to account for epistemic uncertainty arising from limited data, market illiquidity, and structural misspecification. Using
α
-cut decomposition, the fuzzy pricing problem is reduced to a family of deterministic Heston-type models indexed by the confidence level
α∈[
0,1 ]
. A rigorous theoretical foundation is established by proving the existence, uniqueness, and probabilistic representation of the resulting
α
-level partial differential equations via an adapted Feynman-Kac theorem. To overcome the limitations of grid-based numerical solvers, a Fuzzy Deep Galerkin Method (FDGM) is proposed for solving the
α
-level PDEs and calibrating the model directly to market data. The methodology is applied to copper futures prices, and numerical results demonstrate that the fuzzy Heston model significantly outperforms classical benchmark models in terms of calibration accuracy and robustness. The proposed framework provides a flexible and computationally efficient tool for uncertainty-aware pricing in commodity markets.