IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1409.5801.html
   My bibliography  Save this paper

Pricing and hedging of energy spread options and volatility modulated Volterra processes

Author

Listed:
  • Fred Espen Benth
  • Hanna Zdanowicz

Abstract

We derive the price of a spread option based on two assets which follow a bivariate volatility modulated Volterra process dynamics. Such a price dynamics is particularly relevant in energy markets, modelling for example the spot price of power and gas. Volatility modulated Volterra 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, 2014. "Pricing and hedging of energy spread options and volatility modulated Volterra processes," Papers 1409.5801, arXiv.org.
    • Handle: RePEc:arx:papers:1409.5801
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1409.5801
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    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).
    3. Fred Espen Benth & Giulia Di Nunno & Asma Khedher & Maren Diane Schmeck, 2015. "Pricing of Spread Options on a Bivariate Jump Market and Stability to Model Risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(1), pages 28-62, March.
    4. Fred Espen Benth & Heidar Eyjolfsson, 2015. "Representation and approximation of ambit fields in Hilbert space," Papers 1509.08272, arXiv.org.
    5. Alessandro Gnoatto, 2017. "Coherent Foreign Exchange Market Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-29, February.
    6. Benth, Fred Espen & Koekebakker, Steen, 2015. "Pricing of forwards and other derivatives in cointegrated commodity markets," Energy Economics, Elsevier, vol. 52(PA), pages 104-117.
    7. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2008. "Analysis of Fourier transform valuation formulas and applications," Papers 0809.3405, arXiv.org, revised Sep 2009.
    8. Benth, Fred Espen & Paraschiv, Florentina, 2018. "A space-time random field model for electricity forward prices," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 203-216.
    9. Ilya Molchanov & Michael Schmutz, 2009. "Exchangeability type properties of asset prices," Papers 0901.4914, arXiv.org, revised Apr 2011.
    10. Pham, Viet Son, 2020. "Lévy-driven causal CARMA random fields," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7547-7574.
    11. Wei Wei & Asger Lunde, 2023. "Identifying Risk Factors and Their Premia: A Study on Electricity Prices," Journal of Financial Econometrics, Oxford University Press, vol. 21(5), pages 1647-1679.
    12. Wolfgang Karl Härdle & Brenda López Cabrera & Awdesch Melzer, 2021. "Pricing wind power futures," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(4), pages 1083-1102, August.
    13. Ascione, Giacomo & Mehrdoust, Farshid & Orlando, Giuseppe & Samimi, Oldouz, 2023. "Foreign Exchange Options on Heston-CIR Model Under Lévy Process Framework," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    14. Holger Fink & Stefan Mittnik, 2021. "Quanto Pricing beyond Black–Scholes," JRFM, MDPI, vol. 14(3), pages 1-27, March.
    15. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    16. Corsaro, Stefania & Kyriakou, Ioannis & Marazzina, Daniele & Marino, Zelda, 2019. "A general framework for pricing Asian options under stochastic volatility on parallel architectures," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1082-1095.
    17. Ladokhin, Sergiy & Borovkova, Svetlana, 2021. "Three-factor commodity forward curve model and its joint P and Q dynamics," Energy Economics, Elsevier, vol. 101(C).
    18. Michael Samet & Christian Bayer & Chiheb Ben Hammouda & Antonis Papapantoleon & Ra'ul Tempone, 2022. "Optimal Damping with Hierarchical Adaptive Quadrature for Efficient Fourier Pricing of Multi-Asset Options in L\'evy Models," Papers 2203.08196, arXiv.org, revised Oct 2023.
    19. Benth, Fred Espen & Paraschiv, Florentina, 2016. "A Structural Model for Electricity Forward Prices," Working Papers on Finance 1611, University of St. Gallen, School of Finance.
    20. Enrique Villamor & Pablo Olivares, 2023. "Valuing Exchange Options under an Ornstein-Uhlenbeck Covariance Model," IJFS, MDPI, vol. 11(2), pages 1-24, March.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1409.5801. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.