IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1809.03941.html
   My bibliography  Save this paper

Fast calibration of two-factor models for energy option pricing

Author

Listed:
  • Emanuele Fabbiani
  • Andrea Marziali
  • Giuseppe De Nicolao

Abstract

Energy companies need efficient procedures to perform market calibration of stochastic models for commodities. If the Black framework is chosen for option pricing, the bottleneck of the market calibration is the computation of the variance of the asset. Energy commodities are commonly represented by multi-factor linear models, whose variance obeys a matrix Lyapunov differential equation. In this paper, analytical and numerical methods to derive the variance are discussed: the Lyapunov approach is shown to be more straightforward than ad-hoc derivations found in the literature and can be readily extended to higher-dimensional models. A case study is presented, where the variance of a two-factor mean-reverting model is embedded into the Black formulae and the model parameters are calibrated against listed options. The analytical and numerical method are compared, showing that the former makes the calibration 14 times faster. A Python implementation of the proposed methods is available as open-source software on GitHub.

Suggested Citation

  • Emanuele Fabbiani & Andrea Marziali & Giuseppe De Nicolao, 2018. "Fast calibration of two-factor models for energy option pricing," Papers 1809.03941, arXiv.org, revised Dec 2020.
    • Handle: RePEc:arx:papers:1809.03941
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1809.03941
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Martin Barlow & Yuri Gusev & Manpo Lai, 2004. "Calibration Of Multifactor Models In Electricity Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 101-120.
    2. Joanna Janczura & Rafał Weron, 2012. "Efficient estimation of Markov regime-switching models: An application to electricity spot prices," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(3), pages 385-407, July.
    3. Silvana Musti & Viviana Fanelli, 2008. "Modelling electricity forward curve dynamics in the Italian market," Quaderni DSEMS 20-2008, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia.
    4. De Jong Cyriel, 2006. "The Nature of Power Spikes: A Regime-Switch Approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(3), pages 1-28, September.
    5. Rudiger Kiesel & Gero Schindlmayr & Reik Borger, 2009. "A two-factor model for the electricity forward market," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 279-287.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    7. Weron, Rafal & Janczura, Joanna, 2010. "Efficient estimation of Markov regime-switching models: An application to electricity wholesale market prices," MPRA Paper 26628, University Library of Munich, Germany.
    8. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    9. Huisman, Ronald & Mahieu, Ronald, 2003. "Regime jumps in electricity prices," Energy Economics, Elsevier, vol. 25(5), pages 425-434, September.
    10. Janczura, Joanna & Weron, Rafal, 2010. "An empirical comparison of alternate regime-switching models for electricity spot prices," Energy Economics, Elsevier, vol. 32(5), pages 1059-1073, September.
    11. 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.
    12. Schwartz, Eduardo S, 1997. "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    13. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    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. Joanna Janczura & Rafal Weron, 2012. "Inference for Markov-regime switching models of electricity spot prices," HSC Research Reports HSC/12/01, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    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. Eichler, M. & Türk, D., 2013. "Fitting semiparametric Markov regime-switching models to electricity spot prices," Energy Economics, Elsevier, vol. 36(C), pages 614-624.
    4. Thomas Deschatre & Olivier F'eron & Pierre Gruet, 2021. "A survey of electricity spot and futures price models for risk management applications," Papers 2103.16918, arXiv.org, revised Jul 2021.
    5. Fred Espen Benth & Jūratė Šaltytė Benth & Steen Koekebakker, 2008. "Stochastic Modeling of Electricity and Related Markets," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6811, December.
    6. Andreas Gerster, 2016. "Negative price spikes at power markets: the role of energy policy," Journal of Regulatory Economics, Springer, vol. 50(3), pages 271-289, December.
    7. Joanna Janczura, 2012. "Pricing electricity derivatives within a Markov regime-switching model," Papers 1203.5442, arXiv.org.
    8. Stephen Machin & Olivier Marie & Sunčica Vujić, 2012. "Youth Crime and Education Expansion," German Economic Review, Verein für Socialpolitik, vol. 13(4), pages 366-384, November.
    9. Eichler, M. & Türk, D.D.T., 2012. "Fitting semiparametric Markov regime-switching models to electricity spot prices," Research Memorandum 035, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    10. Janczura, Joanna & Trück, Stefan & Weron, Rafał & Wolff, Rodney C., 2013. "Identifying spikes and seasonal components in electricity spot price data: A guide to robust modeling," Energy Economics, Elsevier, vol. 38(C), pages 96-110.
    11. Gerster, Andreas, 2016. "Negative price spikes at power markets: The role of energy policy," Ruhr Economic Papers 636, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    12. Joanna Janczura, 2014. "Pricing electricity derivatives within a Markov regime-switching model: a risk premium approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(1), pages 1-30, February.
    13. Hendrik Kohrs & Hermann Mühlichen & Benjamin R. Auer & Frank Schuhmacher, 2019. "Pricing and risk of swing contracts in natural gas markets," Review of Derivatives Research, Springer, vol. 22(1), pages 77-167, April.
    14. Nowotarski, Jakub & Tomczyk, Jakub & Weron, Rafał, 2013. "Robust estimation and forecasting of the long-term seasonal component of electricity spot prices," Energy Economics, Elsevier, vol. 39(C), pages 13-27.
    15. Bujar Huskaj & Marcus Nossman, 2013. "A Term Structure Model for VIX Futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(5), pages 421-442, May.
    16. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    17. Weron, Rafał & Zator, Michał, 2015. "A note on using the Hodrick–Prescott filter in electricity markets," Energy Economics, Elsevier, vol. 48(C), pages 1-6.
    18. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    19. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    20. 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.

    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:1809.03941. 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.