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Valuation of Spark-Spread Option Written on Electricity and Gas Forward Contracts Under Two-Factor Models with Non-Gaussian Lévy Processes

Author

Listed:
  • Farshid Mehrdoust

    (University of Guilan)

  • Idin Noorani

    (University of Guilan)

Abstract

In energy markets, especially electricity and gas, one experience rather large and dramatic spikes in spot prices, but they are quickly reverting back. Hence it is appropriate to take into account the factors for the spike behavior observed in the spot price series, while other factors induce price evolution when the market is stable. To illustrate this issue, we analyze the dynamics of spikes and seasonality through a normal probability test for returns of spot prices. We propose two-factor model separately for gas and electricity markets, such that in both market model the logarithmic spot price is a stationary Ornstein-Uhlenbeck process and the long-term variations are a drifted Brownian motion. We derive the forward price and its dynamic under proposed model and prove the uniqueness of solution of the stochastic differential equation related to forward price. Then we price the spark-spread option written on electricity and gas forward contracts. In the following, we derive the spark-spread option price under a hybrid geometric Brownian motion and prove that it converges to the sparks-spread option price under the proposed two-factor model. Since the market model is incomplete, we apply the quadratic hedging strategy which minimizes the hedging error. We also investigate the convergence of this strategy through the spark-spread option under the hybrid geometric Brownian motion. Numerical results confirm the achievement of all these convergences. In order to estimate the model parameters, we consider the Lévy processes as the independent normal inverse Gaussian processes and independent compound Poisson processes which have the jump size with the exponential distribution.

Suggested Citation

  • Farshid Mehrdoust & Idin Noorani, 2023. "Valuation of Spark-Spread Option Written on Electricity and Gas Forward Contracts Under Two-Factor Models with Non-Gaussian Lévy Processes," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 807-853, February.
    • Handle: RePEc:kap:compec:v:61:y:2023:i:2:d:10.1007_s10614-021-10232-4
    DOI: 10.1007/s10614-021-10232-4
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    References listed on IDEAS

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    1. Alvaro Cartea & Marcelo Figueroa, 2005. "Pricing in Electricity Markets: A Mean Reverting Jump Diffusion Model with Seasonality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 313-335.
    2. 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.
    3. 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.
    4. Huisman, Ronald & Mahieu, Ronald, 2003. "Regime jumps in electricity prices," Energy Economics, Elsevier, vol. 25(5), pages 425-434, September.
    5. repec:dau:papers:123456789/11500 is not listed on IDEAS
    6. Ole E. Barndorff–Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2010. "Modelling electricity forward markets by ambit fields," CREATES Research Papers 2010-41, Department of Economics and Business Economics, Aarhus University.
    7. Benth Fred E & Saltyte-Benth Jurate, 2006. "Analytical Approximation for the Price Dynamics of Spark Spread Options," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(3), pages 1-28, September.
    8. 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, August.
    9. Hendrik Bessembinder & Michael L. Lemmon, 2002. "Equilibrium Pricing and Optimal Hedging in Electricity Forward Markets," Journal of Finance, American Finance Association, vol. 57(3), pages 1347-1382, June.
    10. Ole Barndorff-Nielsen & Elisa Nicolato & Neil Shephard, 2002. "Some recent developments in stochastic volatility modelling," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 11-23.
    11. Eduardo Schwartz & James E. Smith, 2000. "Short-Term Variations and Long-Term Dynamics in Commodity Prices," Management Science, INFORMS, vol. 46(7), pages 893-911, July.
    12. Ali Hortaçsu & Steven L. Puller, 2008. "Understanding strategic bidding in multi‐unit auctions: a case study of the Texas electricity spot market," RAND Journal of Economics, RAND Corporation, vol. 39(1), pages 86-114, March.
    13. 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.
    14. Nomikos, Nikos K. & Soldatos, Orestes A., 2010. "Analysis of model implied volatility for jump diffusion models: Empirical evidence from the Nordpool market," Energy Economics, Elsevier, vol. 32(2), pages 302-312, March.
    15. Noufel Frikha & Vincent Lemaire, 2013. "Joint Modelling of Gas and Electricity Spot Prices," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(1), pages 69-93, March.
    16. Viviana Fanelli & Maren Diane Schmeck, 2019. "On the seasonality in the implied volatility of electricity options," Quantitative Finance, Taylor & Francis Journals, vol. 19(8), pages 1321-1337, August.
    17. Fred Espen Benth & Jan Kallsen & Thilo Meyer-Brandis, 2007. "A Non-Gaussian Ornstein-Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(2), pages 153-169.
    18. 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.
    19. 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.
    20. 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.
    21. Benth, Fred Espen & Koekebakker, Steen, 2008. "Stochastic modeling of financial electricity contracts," Energy Economics, Elsevier, vol. 30(3), pages 1116-1157, May.
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    Cited by:

    1. Mehrdoust, Farshid & Noorani, Idin & Kanniainen, Juho, 2024. "Valuation of option price in commodity markets described by a Markov-switching model: A case study of WTI crude oil market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 228-269.

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