## Subordinated Levy Processes and Applications to Crude Oil Options

_IMF Working Papers, September 1, 2005_

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**Canonical URL:** [Subordinated Levy Processes and Applications to Crude Oil Options](https://www.imf.org/en/publications/wp/issues/2016/12/31/subordinated-levy-processes-and-applications-to-crude-oil-options-18459)

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## Bibliographic details
- Authors: Noureddine Krichene
- Published: September 1, 2005
- Series: IMF Working Papers
- DOI: https://doi.org/10.5089/9781451861938.001

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### Summary
- One approach to oil markets is to treat oil as an asset, besides its role as a commodity.
- Speculative and nonspeculative activity by investors in the derivatives markets could be responsible for a sizable increase in oil prices.
- The paper recognizes both the consumption and investment aspects of crude oil and proposes Levy processes for modeling uncertainty and options pricing.
- Calibration to crude oil futures' options shows high volatility of oil futures prices, fat-tailed, and right-skewed market expectations, implying a higher probability mass on crude oil prices remaining above the futures' level.
- These findings support the view that demand for futures contracts by investors could lead to excessively high price volatility.

### Methodology
- Proposes Levy processes to model uncertainty in crude oil prices and to price options on crude oil futures.
- Calibration conducted to crude oil futures' options (details of calibration procedure are described in the working paper).

### Key Findings
- High volatility of oil futures prices is observed in the calibrated models.
- Market expectations are fat-tailed.
- Market expectations are right-skewed, implying a higher probability mass on crude oil prices remaining above the futures' level.
- The behavior of investors’ demand for futures contracts can contribute to excessive price volatility.

### Policy and Analytical Implications
- Recognizing crude oil both as a consumption good and as an investable asset is important for understanding price dynamics.
- Derivatives market activity (both speculative and nonspeculative) can materially affect spot and futures price volatility.
- Models that capture fat tails and skewness (such as subordinated Levy processes) provide better characterization of market expectations and risk for option pricing.

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## Content in this bundle

- **Crude oil prices density forecast on July, 5, 2005 for end-September 2005.**
  - [Crude oil prices density forecast on July, 5, 2005 for end-September 2005. (Markdown version)](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp05174.pdf.md){rel="alternate" type="text/markdown"}
  - [Crude oil prices density forecast on July, 5, 2005 for end-September 2005. (PDF)](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp05174.pdf){rel="external" type="application/pdf"}

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_Source: https://www.imf.org/en/publications/wp/issues/2016/12/31/subordinated-levy-processes-and-applications-to-crude-oil-options-18459_