Evaluating Microscopic and Macroscopic Models for Derivative Contracts on Commodity Indices

ArXiv ID: 2408.00784 “View on arXiv”

Authors: Unknown

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.

Keywords: Commodity Index Derivatives, Microscopic vs Macroscopic Modeling, Autocallable Options, Sensitivities Analysis, Calibration, Commodities

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail
  • Why: The paper employs advanced mathematical modeling (Stochastic Local Volatility, SDEs) and complex calibration procedures, while also providing rigorous empirical testing with real market data (S&P GSCI Crude Oil), calibration comparisons, and sensitivity analysis on specific derivative contracts.
  flowchart TD
    A["Research Goal:<br>Compare Microscopic vs Macroscopic<br>Modeling for Commodity Index Derivatives"] --> B["Input Data:<br>S&P GSCI Crude Oil Excess-Return<br>Index & Derivative Prices"]

    B --> C["Methodology:<br>Calibrate Both Models<br>to Market Data"]

    C --> D["Computational Process:<br>Pricing & Sensitivity Analysis<br>on Autocallable Options"]

    D --> E["Key Findings:<br>Microscopic: Flexible but complex<br>calibration<br>Macroscopic: Practical but questions<br>on futures curve dynamics"]