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Asymptotic Pricing of Commodity Derivatives using Stochastic Volatility Spot Models

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  • Samuel Hikspoors
  • Sebastian Jaimungal
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    Abstract

    It is well known that stochastic volatility is an essential feature of commodity spot prices. By using methods of singular perturbation theory, we obtain approximate but explicit closed-form pricing equations for forward contracts and options on single- and two-name forward prices. The expansion methodology is based on a fast mean-reverting stochastic volatility driving factor and leads to pricing results in terms of constant volatility prices, their Deltas and their Delta-Gammas. Both the standard single-factor mean-reverting spot model and a two-factor generalization, in which the long-run mean is itself mean-reverting, are extended to include stochastic volatility and each is analysed in detail. The stochastic volatility corrections can be used to efficiently calibrate option prices and compute sensitivities.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802170432
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 15 (2008)
    Issue (Month): 5-6 ()
    Pages: 449-477

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    Handle: RePEc:taf:apmtfi:v:15:y:2008:i:5-6:p:449-477

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    Web page: http://www.tandfonline.com/RAMF20

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    Web: http://www.tandfonline.com/pricing/journal/RAMF20

    Related research

    Keywords: Commodity derivatives; stochastic volatility; spread options; singular perturbation methods;

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    Cited by:
    1. Ole E. Barndorff-Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2013. "Modelling energy spot prices by volatility modulated L\'{e}vy-driven Volterra processes," Papers 1307.6332, arXiv.org.
    2. Álvaro Cartea & Carlos González-Pedraz, 2010. "How much should we pay for interconnecting electricity markets? A real options approach," Business Economics Working Papers wb103206, Universidad Carlos III, Departamento de Economía de la Empresa.
    3. Chi, Yichun & Jaimungal, Sebastian & Lin, X. Sheldon, 2010. "An insurance risk model with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 52-66, February.

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