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Modelling spikes and pricing swing options in electricity markets


  • Ben Hambly
  • Sam Howison
  • Tino Kluge


Most electricity markets exhibit high volatilities and occasional distinctive price spikes, which result in demand for derivative products which protect the holder against high prices. In this paper we examine a simple spot price model that is the exponential of the sum of an Ornstein-Uhlenbeck and an independent mean-reverting pure jump process. We derive the moment generating function as well as various approximations to the probability density function of the logarithm of the spot price process at maturity T. Hence we are able to calibrate the model to the observed forward curve and present semi-analytic formulae for premia of path-independent options as well as approximations to call and put options on forward contracts with and without a delivery period. In order to price path-dependent options with multiple exercise rights like swing contracts a grid method is utilized which in turn uses approximations to the conditional density of the spot process.

Suggested Citation

  • Ben Hambly & Sam Howison & Tino Kluge, 2009. "Modelling spikes and pricing swing options in electricity markets," Quantitative Finance, Taylor & Francis Journals, vol. 9(8), pages 937-949.
  • Handle: RePEc:taf:quantf:v:9:y:2009:i:8:p:937-949 DOI: 10.1080/14697680802596856

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    References listed on IDEAS

    1. Terasvirta, T & Anderson, H M, 1992. "Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 119-136, Suppl. De.
    2. Neftci, Salih N, 1984. "Are Economic Time Series Asymmetric over the Business Cycle?," Journal of Political Economy, University of Chicago Press, vol. 92(2), pages 307-328, April.
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    Cited by:

    1. Marcus Eriksson & Jukka Lempa & Trygve Nilssen, 2014. "Swing options in commodity markets: a multidimensional Lévy diffusion model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(1), pages 31-67, February.
    2. Cartea, Álvaro & González-Pedraz, Carlos, 2012. "How much should we pay for interconnecting electricity markets? A real options approach," Energy Economics, Elsevier, vol. 34(1), pages 14-30.
    3. Bannör, Karl & Kiesel, Rüdiger & Nazarova, Anna & Scherer, Matthias, 2016. "Parametric model risk and power plant valuation," Energy Economics, Elsevier, vol. 59(C), pages 423-434.
    4. repec:spr:compst:v:79:y:2014:i:1:p:31-67 is not listed on IDEAS
    5. Tiziano De Angelis & Yerkin Kitapbayev, 2014. "On the optimal exercise boundaries of swing put options," Papers 1407.6860,, revised Jan 2017.
    6. Miha Troha & Raphael Hauser, 2014. "Calculation of a power price equilibrium," Papers 1409.6645,
    7. repec:eee:eneeco:v:67:y:2017:i:c:p:496-507 is not listed on IDEAS
    8. Leif Andersen, 2010. "Markov models for commodity futures: theory and practice," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 831-854.
    9. 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.
    10. Coulon, Michael & Powell, Warren B. & Sircar, Ronnie, 2013. "A model for hedging load and price risk in the Texas electricity market," Energy Economics, Elsevier, vol. 40(C), pages 976-988.
    11. de Oliveira, Denis Luis & Brandao, Luiz E. & Igrejas, Rafael & Gomes, Leonardo Lima, 2014. "Switching outputs in a bioenergy cogeneration project: A real options approach," Renewable and Sustainable Energy Reviews, Elsevier, vol. 36(C), pages 74-82.
    12. Patrick Henaff & Ismail Laachir & Francesco Russo, 2013. "Gas storage valuation and hedging. A quantification of the model risk," Papers 1312.3789,
    13. Farkas, Walter & Gourier, Elise & Huitema, Robert & Necula, Ciprian, 2017. "A two-factor cointegrated commodity price model with an application to spread option pricing," Journal of Banking & Finance, Elsevier, vol. 77(C), pages 249-268.
    14. Caldana, Ruggero & Fusai, Gianluca, 2013. "A general closed-form spread option pricing formula," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4893-4906.


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