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Pricing and hedging Asian-style options on energy

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  • Fred Benth
  • Nils Detering

Abstract

We solve the problem of pricing and hedging Asian-style options on energy with a quadratic risk criterion when trading in the underlying future is restricted. Liquid trading in the future is only possible up to the start of a so-called delivery period. After the start of the delivery period, the hedge positions cannot be adjusted any more until maturity. This reflects the trading situation at the Nordic energy market Nord Pool, for example. We show that there exists a unique solution to this combined continuous–discrete quadratic hedging problem if the future price process is a special semimartingale with bounded mean–variance tradeoff. Additionally, under the assumption that the future price process is a local martingale, the hedge positions before the averaging period are inherited from the market specification without trading restriction. As an application, we consider three models and derive their quadratic hedge positions in explicit form: a simple Black–Scholes model with time-dependent volatility, the stochastic volatility model of Barndorff-Nielsen and Shephard, and an exponential additive model. Based on an exponential spot price model driven by two NIG Lévy processes, we determine an exponential additive model for the future price by moment matching techniques. We calculate hedge positions and determine the quadratic hedging error in a simulation study. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Fred Benth & Nils Detering, 2015. "Pricing and hedging Asian-style options on energy," Finance and Stochastics, Springer, vol. 19(4), pages 849-889, October.
    • Handle: RePEc:spr:finsto:v:19:y:2015:i:4:p:849-889
    DOI: 10.1007/s00780-015-0270-2
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    References listed on IDEAS

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    6. 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.
    7. Rüdiger Kiesel & Matthias Scherer & Rudi Zagst (ed.), 2010. "Alternative Investments and Strategies," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7373, January.
    8. St'ephane Goutte & Nadia Oudjane & Francesco Russo, 2012. "Variance Optimal Hedging for discrete time processes with independent increments. Application to Electricity Markets," Papers 1205.4089, arXiv.org.
    9. Schweizer, Martin, 1992. "Martingale densities for general asset prices," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 363-378.
    10. Weron, Rafal, 2008. "Market price of risk implied by Asian-style electricity options and futures," Energy Economics, Elsevier, vol. 30(3), pages 1098-1115, May.
    11. Jan Vecer & Mingxin Xu, 2004. "Pricing Asian options in a semimartingale model," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 170-175.
    12. 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.
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    Citations

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    Cited by:

    1. Panagiotis Christodoulou & Nils Detering & Thilo Meyer-Brandis, 2018. "Local Risk-Minimization With Multiple Assets Under Illiquidity With Applications In Energy Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-44, June.
    2. Takuji Arai & Yuto Imai & Ryoichi Suzuki, 2017. "Local risk-minimization for Barndorff-Nielsen and Shephard models," Finance and Stochastics, Springer, vol. 21(2), pages 551-592, April.
    3. Adland, Roar & Benth, Fred Espen & Koekebakker, Steen, 2018. "Multivariate modeling and analysis of regional ocean freight rates," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 113(C), pages 194-221.
    4. Müller, Gernot & Seibert, Armin, 2019. "Bayesian estimation of stable CARMA spot models for electricity prices," Energy Economics, Elsevier, vol. 78(C), pages 267-277.
    5. Panagiotis Christodoulou & Nils Detering & Thilo Meyer-Brandis, 2017. "Local risk-minimization with multiple assets under illiquidity with applications in energy markets," Papers 1705.06918, arXiv.org, revised Jun 2018.
    6. Elisa Alòs & Jorge A. León, 2019. "A note on the implied volatility of floating strike Asian options," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 743-758, December.

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    More about this item

    Keywords

    Asian options; Energy markets; Trading restrictions; Quadratic hedging; Moment matching; 91G20; 60G99; C61; G11; G12; G13;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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