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A hybrid commodity and interest rate market model

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  • K. F. Pilz
  • E. Schlögl

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.

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  • K. F. Pilz & E. Schlögl, 2013. "A hybrid commodity and interest rate market model," Quantitative Finance, Taylor & Francis Journals, vol. 13(4), pages 543-560, March.
    • Handle: RePEc:taf:quantf:v:13:y:2013:i:4:p:543-560
    DOI: 10.1080/14697688.2011.627879
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    References listed on IDEAS

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    1. K. R. Miltersen, 2003. "Commodity price modelling that matches current observables: a new approach," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 51-58.
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    3. Erik Schlögl, 2001. "Arbitrage-Free Interpolation in Models of Market Observable Interest Rates," Research Paper Series 71, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Cited by:

    1. Patrik Karlsson & Kay F Pilz & Erik Schlogl, 2016. "Calibrating Market Model to Commodity and Interest Rate Risk," Research Paper Series 372, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Papers 1801.04994, arXiv.org, revised Feb 2018.
    3. Benjamin Tin Chun Cheng, 2017. "Pricing and Hedging of Long-Dated Commodity Derivatives," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2017.
    4. repec:uts:finphd:37 is not listed on IDEAS
    5. José Luis Fernández & Marta Pou & Carlos Vázquez, 2015. "A drift‐free simulation method for pricing commodity derivatives," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(4), pages 536-550, July.
    6. Emanuele Nastasi & Andrea Pallavicini & Giulio Sartorelli, 2020. "Smile Modeling In Commodity Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(03), pages 1-28, May.
    7. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Risks, MDPI, vol. 6(1), pages 1-39, March.
    8. Cheng, Benjamin & Nikitopoulos, Christina Sklibosios & Schlögl, Erik, 2018. "Pricing of long-dated commodity derivatives: Do stochastic interest rates matter?," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 148-166.
    9. Benjamin Cheng & Christina Nikitopoulos-Sklibosios & Erik Schlogl, 2015. "Pricing of Long-dated Commodity Derivatives with Stochastic Volatility and Stochastic Interest Rates," Research Paper Series 366, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. P. Karlsson & K. F. Pilz & E. Schlögl, 2017. "Calibrating a market model with stochastic volatility to commodity and interest rate risk," Quantitative Finance, Taylor & Francis Journals, vol. 17(6), pages 907-925, June.

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