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A Hybrid Commodity and Interest Rate

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Abstract

A joint model of commodity price and interest rate risk is constructed analogously to the multi-currency LIBOR Market Model (LMM). Going beyond a simple "re-interpretation" of the multi-currency LMM, issues arising in the application of the model to actual commodity market data are specifically addressed. Firstly, liquid market prices are only available for options on commodity futures, rather than forwards, thus the difference between forward and futures prices must be explicitly taken into account in the calibration. Secondly, we construct a procedure to achieve a consistent fit of the model to market data for interest options, commodity options and historically estimated correlations between interest rates and commodity prices. We illustrate the model by an application to real market data and derive pricing formulas for commodity spread options.

Suggested Citation

  • Kay Pilz & Erik Schlogl, 2009. "A Hybrid Commodity and Interest Rate," Research Paper Series 261, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:261
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    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp261.pdf
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    References listed on IDEAS

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    1. Erik Schlögl, 2002. "A multicurrency extension of the lognormal interest rate Market Models," Finance and Stochastics, Springer, vol. 6(2), pages 173-196.
    2. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
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    Cited by:

    1. Kay Pilz & Erik Schlogl, 2010. "Calibration of Multicurrency LIBOR Market Models," Research Paper Series 286, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Benjamin Cheng & Christina Nikitopoulos-Sklibosios & Erik Schlogl, 2016. "Empirical Pricing Performance in Long-Dated Crude Oil Derivatives: Do Models with Stochastic Interest Rates Matter?," Research Paper Series 367, Quantitative Finance Research Centre, University of Technology, Sydney.

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    Keywords

    Commodity modeling; LIBOR Market Model; commodity futures; interest rate risk; spread options;

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