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Pricing And Hedging Of Energy Spread Options And Volatility Modulated Volterra Processes

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  • FRED ESPEN BENTH

    (Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway2Centre of Advanced Study, Drammensveien 78, N-0271 Oslo, Norway)

  • HANNA ZDANOWICZ

    (Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway)

Abstract

We derive the price of a spread option based on two assets which follow a bivariate volatility modulated Volterra (VMV) process dynamics. Such a price dynamics is particularly relevant in energy markets, modeling for example the spot price of power and gas. VMV processes are in general not semimartingales, but contain several special cases of interest in energy markets, like for example continuous-time autoregressive moving average processes. Based on a change of measure, we obtain a pricing expression based on a univariate Fourier transform of the payoff function and the characteristic function of the price dynamics. Moreover, the spread option price can be expressed in terms of the forward prices on the underlying dynamics assets. We compute a linear system of equations for the quadratic hedge for the spread option in terms of a portfolio of underlying forward contracts.

Suggested Citation

  • Fred Espen Benth & Hanna Zdanowicz, 2016. "Pricing And Hedging Of Energy Spread Options And Volatility Modulated Volterra Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-22, February.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:01:n:s0219024916500023
    DOI: 10.1142/S0219024916500023
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    References listed on IDEAS

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    1. Ernst Eberlein & Antonis Papapantoleon & Albert Shiryaev, 2008. "On the duality principle in option pricing: semimartingale setting," Finance and Stochastics, Springer, vol. 12(2), pages 265-292, April.
    2. 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.
    3. Matt Thompson, 2013. "Optimal Economic Dispatch and Risk Management of Thermal Power Plants in Deregulated Markets," Operations Research, INFORMS, vol. 61(4), pages 791-809, August.
    4. Ernst Eberlein & Antonis Papapantoleon & Albert N. Shiryaev, 2008. "Esscher transform and the duality principle for multidimensional semimartingales," Papers 0809.0301, arXiv.org, revised Nov 2009.
    5. Benth, Fred Espen & Klüppelberg, Claudia & Müller, Gernot & Vos, Linda, 2014. "Futures pricing in electricity markets based on stable CARMA spot models," Energy Economics, Elsevier, vol. 44(C), pages 392-406.
    6. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    7. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    8. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2010. "Analysis of Fourier Transform Valuation Formulas and Applications," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(3), pages 211-240.
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    Cited by:

    1. Adriana A. Londoño & Juan D. Velásquez, 2023. "Risk Management in Electricity Markets: Dominant Topics and Research Trends," Risks, MDPI, vol. 11(7), pages 1-13, June.
    2. Deschatre, Thomas & Féron, Olivier & Gruet, Pierre, 2021. "A survey of electricity spot and futures price models for risk management applications," Energy Economics, Elsevier, vol. 102(C).

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