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Risk valuation of quanto derivatives on temperature and electricity

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  • Aur'elien Alfonsi
  • Nerea Vadillo

Abstract

This paper develops a coupled model for day-ahead electricity prices and average daily temperature which allows to model quanto weather and energy derivatives. These products have gained on popularity as they enable to hedge against both volumetric and price risks. Electricity day-ahead prices and average daily temperatures are modelled through non homogeneous Ornstein-Uhlenbeck processes driven by a Brownian motion and a Normal Inverse Gaussian L\'evy process, which allows to include dependence between them. A Conditional Least Square method is developed to estimate the different parameters of the model and used on real data. Then, explicit and semi-explicit formulas are obtained for derivatives including quanto options and compared with Monte Carlo simulations. Last, we develop explicit formulas to hedge statically single and double sided quanto options by a portfolio of electricity options and temperature options (CDD or HDD).

Suggested Citation

  • Aur'elien Alfonsi & Nerea Vadillo, 2023. "Risk valuation of quanto derivatives on temperature and electricity," Papers 2310.07692, arXiv.org, revised Apr 2024.
    • Handle: RePEc:arx:papers:2310.07692
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    References listed on IDEAS

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    1. Anders B. Trolle & Eduardo S. Schwartz, 2009. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4423-4461, November.
    2. Cao, M. & Wei, J., 1999. "Pricing Weather Derivative : An Equilibrium Approach," Rotman School of Management - Finance 99-002, Rotman School of Management, University of Toronto.
    3. Knittel, Christopher R. & Roberts, Michael R., 2005. "An empirical examination of restructured electricity prices," Energy Economics, Elsevier, vol. 27(5), pages 791-817, September.
    4. 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.
    5. Sean D. Campbell & Francis X. Diebold, 2005. "Weather Forecasting for Weather Derivatives," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 6-16, March.
    6. Caporin, Massimiliano & Preś, Juliusz & Torro, Hipolit, 2012. "Model based Monte Carlo pricing of energy and temperature Quanto options," Energy Economics, Elsevier, vol. 34(5), pages 1700-1712.
    7. 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.
    8. 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.
    9. Peter Alaton & Boualem Djehiche & David Stillberger, 2002. "On modelling and pricing weather derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(1), pages 1-20.
    10. Fred Espen Benth & Jūratė Šaltytė Benth, 2012. "Modeling and Pricing in Financial Markets for Weather Derivatives," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8457.
    11. Patrick L. Brockett & Mulong Wang & Chuanhou Yang, 2005. "Weather Derivatives and Weather Risk Management," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 8(1), pages 127-140, March.
    12. 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).
    13. Weron, Rafal & Misiorek, Adam, 2008. "Forecasting spot electricity prices: A comparison of parametric and semiparametric time series models," International Journal of Forecasting, Elsevier, vol. 24(4), pages 744-763.
    14. 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.
    15. Francisco Pérez-González & Hayong Yun, 2013. "Risk Management and Firm Value: Evidence from Weather Derivatives," Journal of Finance, American Finance Association, vol. 68(5), pages 2143-2176, October.
    16. Gibson, Rajna & Schwartz, Eduardo S, 1990. "Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-976, July.
    17. Yuji Yamada & Takuji Matsumoto, 2023. "Construction of Mixed Derivatives Strategy for Wind Power Producers," Energies, MDPI, vol. 16(9), pages 1-26, April.
    18. Larsson, Karl, 2023. "Parametric heat wave insurance," Journal of Commodity Markets, Elsevier, vol. 31(C).
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