IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v15y2008i4p355-386.html
   My bibliography  Save this article

Modelling the Temperature Time-dependent Speed of Mean Reversion in the Context of Weather Derivatives Pricing

Author

Listed:
  • A. Zapranis
  • A. Alexandridis

Abstract

In this paper, in the context of an Ornstein-Uhlenbeck temperature process, we use neural networks to examine the time dependence of the speed of the mean reversion parameter α of the process. We estimate non-parametrically with a neural network a model of the temperature process and then compute the derivative of the network output w.r.t. the network input, in order to obtain a series of daily values for α. To our knowledge, this is the first time that this has been done, and it gives us a much better insight into the temperature dynamics and temperature derivative pricing. Our results indicate strong time dependence in the daily values of α, and no seasonal patterns. This is important, since in all relevant studies performed thus far, α was assumed to be constant. Furthermore, the residuals of the neural network provide a better fit to the normal distribution when compared with the residuals of the classic linear models used in the context of temperature modelling (where α is constant). It follows that by setting the mean reversion parameter to be a function of time we improve the accuracy of the pricing of the temperature derivatives. Finally, we provide the pricing equations for temperature futures, when α is time dependent.

Suggested Citation

  • A. Zapranis & A. Alexandridis, 2008. "Modelling the Temperature Time-dependent Speed of Mean Reversion in the Context of Weather Derivatives Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(4), pages 355-386.
    • Handle: RePEc:taf:apmtfi:v:15:y:2008:i:4:p:355-386
    DOI: 10.1080/13504860802006065
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802006065
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/13504860802006065?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. M. Davis, 2001. "Pricing weather derivatives by marginal value," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 305-308, March.
    2. Fred ESPEN Benth & Jurate saltyte Benth, 2007. "The volatility of temperature and pricing of weather derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 553-561.
    3. MacKinnon, James G, 1996. "Numerical Distribution Functions for Unit Root and Cointegration Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 601-618, Nov.-Dec..
    4. Fred Espen Benth & Jurate Saltyte-Benth, 2005. "Stochastic Modelling of Temperature Variations with a View Towards Weather Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(1), pages 53-85.
    5. Jewson,Stephen & Brix,Anders, 2005. "Weather Derivative Valuation," Cambridge Books, Cambridge University Press, number 9780521843713, September.
    6. Sailor, David J. & Muñoz, J.Ricardo, 1997. "Sensitivity of electricity and natural gas consumption to climate in the U.S.A.—Methodology and results for eight states," Energy, Elsevier, vol. 22(10), pages 987-998.
    7. Dorje Brody & Joanna Syroka & Mihail Zervos, 2002. "Dynamical pricing of weather derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 2(3), pages 189-198.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ahmed, Walid M.A., 2022. "On the higher-order moment interdependence of stock and commodity markets: A wavelet coherence analysis," The Quarterly Review of Economics and Finance, Elsevier, vol. 83(C), pages 135-151.
    2. Hainaut, Donatien, 2018. "Hedging of crop harvest with derivatives on temperature," LIDAM Discussion Papers ISBA 2018012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Gunther Leobacher & Philip Ngare, 2011. "On Modelling and Pricing Rainfall Derivatives with Seasonality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(1), pages 71-91.
    4. Ahmet Göncü, 2013. "Comparison of temperature models using heating and cooling degree days futures," Journal of Risk Finance, Emerald Group Publishing, vol. 14(2), pages 159-178, February.
    5. Rui Zhou & Johnny Siu-Hang Li & Jeffrey Pai, 2019. "Pricing temperature derivatives with a filtered historical simulation approach," The European Journal of Finance, Taylor & Francis Journals, vol. 25(15), pages 1462-1484, October.
    6. Andrea Barth & Fred Espen Benth & Jurgen Potthoff, 2011. "Hedging of Spatial Temperature Risk with Market-Traded Futures," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(2), pages 93-117.
    7. A. Alexandridis & A. Zapranis, 2013. "Wind Derivatives: Modeling and Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 41(3), pages 299-326, March.
    8. Cui, Hairong & Zhou, Ying & Dzandu, Michael D. & Tang, Yinshan & Lu, Xunfa, 2019. "Is temperature-index derivative suitable for China?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    9. Dorfleitner, Gregor & Wimmer, Maximilian, 2010. "The pricing of temperature futures at the Chicago Mercantile Exchange," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1360-1370, June.
    10. Frank Schiller & Gerold Seidler & Maximilian Wimmer, 2012. "Temperature models for pricing weather derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 12(3), pages 489-500, March.
    11. Evarest Emmanuel & Berntsson Fredrik & Singull Martin & Yang Xiangfeng, 2018. "Weather derivatives pricing using regime switching model," Monte Carlo Methods and Applications, De Gruyter, vol. 24(1), pages 13-27, March.
    12. Yonatan Berman & Eshel Ben-Jacob & Xin Zhang & Yoash Shapira, 2016. "Analyzing the Long Term Cohesive Effect of Sector Specific Driving Forces," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-16, March.
    13. Wei Yuan & Ahmet Göncü & Giray Ökten, 2015. "Estimating sensitivities of temperature-based weather derivatives," Applied Economics, Taylor & Francis Journals, vol. 47(19), pages 1942-1955, April.
    14. 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, August.
    15. Šaltytė Benth, Jūratė & Benth, Fred Espen, 2012. "A critical view on temperature modelling for application in weather derivatives markets," Energy Economics, Elsevier, vol. 34(2), pages 592-602.
    16. Tellez Gaytán, Jesús Cuauhtémoc & Serrano Acevedo, María Eugenia & Rico Arias, Jaime Ángel, 2014. "Modelación del clima bajo un proceso estocástico de reversión a la media estacional / Modeling weather under a seasonal mean reversion stochastic process," Estocástica: finanzas y riesgo, Departamento de Administración de la Universidad Autónoma Metropolitana Unidad Azcapotzalco, vol. 4(1), pages 9-32, enero-jun.
    17. Eirini Konstantinidi & Gkaren Papazian & George Skiadopoulos, 2015. "Modeling the Dynamics of Temperature with a View to Weather Derivatives," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 17, pages 511-544, World Scientific Publishing Co. Pte. Ltd..
    18. Yuji Yamada & Takuji Matsumoto, 2023. "Construction of Mixed Derivatives Strategy for Wind Power Producers," Energies, MDPI, vol. 16(9), pages 1-26, April.
    19. Alexandridis, Antonis K. & Kampouridis, Michael & Cramer, Sam, 2017. "A comparison of wavelet networks and genetic programming in the context of temperature derivatives," International Journal of Forecasting, Elsevier, vol. 33(1), pages 21-47.
    20. Beyazıt, Mehmet Fuat & Koc, Erdogan, 2010. "An analysis of snow options for ski resort establishments," Tourism Management, Elsevier, vol. 31(5), pages 676-683.
    21. Hainaut, Donatien, 2019. "Hedging of crop harvest with derivatives on temperature," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 98-114.

    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. Dorfleitner, Gregor & Wimmer, Maximilian, 2010. "The pricing of temperature futures at the Chicago Mercantile Exchange," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1360-1370, June.
    2. Alexandridis, Antonis K. & Kampouridis, Michael & Cramer, Sam, 2017. "A comparison of wavelet networks and genetic programming in the context of temperature derivatives," International Journal of Forecasting, Elsevier, vol. 33(1), pages 21-47.
    3. Rui Zhou & Johnny Siu-Hang Li & Jeffrey Pai, 2019. "Pricing temperature derivatives with a filtered historical simulation approach," The European Journal of Finance, Taylor & Francis Journals, vol. 25(15), pages 1462-1484, October.
    4. Cui, Hairong & Zhou, Ying & Dzandu, Michael D. & Tang, Yinshan & Lu, Xunfa, 2019. "Is temperature-index derivative suitable for China?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    5. 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, August.
    6. Elias, R.S. & Wahab, M.I.M. & Fang, L., 2014. "A comparison of regime-switching temperature modeling approaches for applications in weather derivatives," European Journal of Operational Research, Elsevier, vol. 232(3), pages 549-560.
    7. Ahčan, Aleš, 2012. "Statistical analysis of model risk concerning temperature residuals and its impact on pricing weather derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 131-138.
    8. 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.
    9. Frank Schiller & Gerold Seidler & Maximilian Wimmer, 2012. "Temperature models for pricing weather derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 12(3), pages 489-500, March.
    10. 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.
    11. Jr‐Wei Huang & Sharon S. Yang & Chuang‐Chang Chang, 2018. "Modeling temperature behaviors: Application to weather derivative valuation," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(9), pages 1152-1175, September.
    12. Evarest Emmanuel & Berntsson Fredrik & Singull Martin & Yang Xiangfeng, 2018. "Weather derivatives pricing using regime switching model," Monte Carlo Methods and Applications, De Gruyter, vol. 24(1), pages 13-27, March.
    13. Andrea Barth & Fred Espen Benth & Jurgen Potthoff, 2011. "Hedging of Spatial Temperature Risk with Market-Traded Futures," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(2), pages 93-117.
    14. Eirini Konstantinidi & Gkaren Papazian & George Skiadopoulos, 2015. "Modeling the Dynamics of Temperature with a View to Weather Derivatives," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 17, pages 511-544, World Scientific Publishing Co. Pte. Ltd..
    15. Šaltytė Benth, Jūratė & Benth, Fred Espen, 2012. "A critical view on temperature modelling for application in weather derivatives markets," Energy Economics, Elsevier, vol. 34(2), pages 592-602.
    16. repec:hum:wpaper:sfb649dp2009-046 is not listed on IDEAS
    17. Benth, Fred & Härdle, Wolfgang Karl & López Cabrera, Brenda, 2009. "Pricing of Asian temperature risk," SFB 649 Discussion Papers 2009-046, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    18. Ritter, Matthias & Mußhoff, Oliver & Odening, Martin, 2010. "Meteorological forecasts and the pricing of weather derivatives," SFB 649 Discussion Papers 2010-043, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    19. Samuel Asante Gyamerah & Philip Ngare & Dennis Ikpe, 2018. "Regime-Switching Temperature Dynamics Model for Weather Derivatives," International Journal of Stochastic Analysis, Hindawi, vol. 2018, pages 1-15, July.
    20. Wolfgang Karl Härdle & Brenda López Cabrera, 2012. "The Implied Market Price of Weather Risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(1), pages 59-95, February.
    21. Július Bemš & Caner Aydin, 2022. "Introduction to weather derivatives," Wiley Interdisciplinary Reviews: Energy and Environment, Wiley Blackwell, vol. 11(3), May.

    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:taf:apmtfi:v:15:y:2008:i:4:p:355-386. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RAMF20 .

    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.