Pricing commodity index options

Abstract

We present a stochastic local volatility model for derivative contracts on commodity futures. The aim of the model is to recover the prices of derivative claims both on future contracts and on indices on future strategies. Numerical examples for calibration and pricing are provided for the S&P GSCI Crude Oil excess-return index.

Keywords:

• Commodity futures
• Commodity indices
• Option pricing
• Stochastic local volatility
• Markov projections

JEL Classification:

• C63
• G13

AMS Classification:

• 65C05
• 91G20
• 91G60

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¶ The opinions here expressed are solely those of the authors and do not represent in any way those of their employers.

† GSCI refers to Goldman Sachs Commodity Index. The white paper describing the index methodology can be found at the S&P web site: https://www.spglobal.com/spdji/en/documents/methodologies/methodology-sp-gsci.pdf.

† The NLopt nonlinear-optimization package is one of the de facto standards for non-linear optimization in various programming languages such as C++, Julia, Rust…The library can be found in http://github.com/stevengj/nlopt and is developed and maintained by Steven G. Johnson.

† Also the Clang and the Intel C++ compilers have been tested obtaining the same or very similar results.

Additional information

Funding

A.P. Manzano-Herrero and C. Vázquez acknowledge the support received from the Centro de Investigación en Tecnologías de la Información y las Comunicaciones de Galicia, CITIC, funded by Xunta de Galicia and the European Union (European Regional Development Fund, Galicia 2014-2020 Program) by grant ED431G 2019/01. Also both authors acknowledge the funding from Xunta de Galicia through the grant ED431C2018/033, ED431C 2022/47, as well as the funding from Spanish Ministry of Science and Innovation with the grant PID2019-10858RB-I00.