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Local Volatility Models in Commodity Markets and Online Calibration

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  • Vinicius Albani
  • Uri M. Ascher
  • Jorge P. Zubelli

Abstract

We introduce a local volatility model for the valuation of options on commodity futures by using European vanilla option prices. The corresponding calibration problem is addressed within an online framework, allowing the use of multiple price surfaces. Since uncertainty in the observation of the underlying future prices translates to uncertainty in data locations, we propose a model-based adjustment of such prices that improves reconstructions and smile adherence. In order to tackle the ill-posedness of the calibration problem we incorporate a priori information through a judiciously designed Tikhonov-type regularization. Extensive empirical tests with market as well as synthetic data are used to demonstrate the effectiveness of the methodology and algorithms.

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  • Vinicius Albani & Uri M. Ascher & Jorge P. Zubelli, 2016. "Local Volatility Models in Commodity Markets and Online Calibration," Papers 1602.04372, arXiv.org.
    • Handle: RePEc:arx:papers:1602.04372
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    References listed on IDEAS

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    1. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    2. repec:dau:papers:123456789/607 is not listed on IDEAS
    3. Bjerksund, Petter & Stensland, Gunnar, 1993. "Closed-form approximation of American options," Scandinavian Journal of Management, Elsevier, vol. 9(Supplemen), pages 87-99.
    4. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. "Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    5. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    6. Helyette Geman, 2005. "Commodities and Commodity Derivatives. Modeling and Pricing for Agriculturals, Metals and Energy," Post-Print halshs-00144182, HAL.
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