  In this article, we analyze two modeling approaches for the pricing of
derivative contracts on a commodity index. The first one is a microscopic
approach, where the components of the index are modeled individually, and the
index price is derived from their combination. The second one is a macroscopic
approach, where the index is modeled directly. While the microscopic approach
offers greater flexibility, its calibration results to be more challenging,
thus leading practitioners to favor the macroscopic approach. However, in the
macroscopic model, the lack of explicit futures curve dynamics raises questions
about its ability to accurately capture the behavior of the index and its
sensitivities. In order to investigate this, we calibrate both models using
derivatives of the S\&P GSCI Crude Oil excess-return index and compare their
pricing and sensitivities on path-dependent options, such as autocallable
contracts. This research provides insights into the suitability of macroscopic
models for pricing and hedging purposes in real scenarios.
