Evaluating Microscopic and Macroscopic Models for Derivative Contracts on Commodity Indices

TL;DR

This paper compares microscopic and macroscopic models for pricing commodity index derivatives, highlighting their calibration challenges, differences in capturing index behavior, and evaluating their effectiveness through empirical analysis.

Contribution

It provides a comparative analysis of microscopic and macroscopic models for commodity index derivatives, focusing on calibration difficulties and practical performance.

Findings

Macroscopic models are easier to calibrate but may lack detailed index dynamics.

Microscopic models offer flexibility but are more complex to calibrate.

Both models are tested on path-dependent options like autocallable contracts.

Abstract

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.