IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v12y2005i1p53-85.html
   My bibliography  Save this article

Stochastic Modelling of Temperature Variations with a View Towards Weather Derivatives

Author

Listed:
  • Fred Espen Benth
  • Jurate Saltyte-Benth

Abstract

Daily average temperature variations are modelled with a mean-reverting Ornstein-Uhlenbeck process driven by a generalized hyperbolic Levy process and having seasonal mean and volatility. It is empirically demonstrated that the proposed dynamics fits Norwegian temperature data quite successfully, and in particular explains the seasonality, heavy tails and skewness observed in the data. The stability of mean-reversion and the question of fractionality of the temperature data are discussed. The model is applied to derive explicit prices for some standardized futures contracts based on temperature indices and options on these traded on the Chicago Mercantile Exchange (CME).

Suggested Citation

  • 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.
    • Handle: RePEc:taf:apmtfi:v:12:y:2005:i:1:p:53-85
    DOI: 10.1080/1350486042000271638
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000271638
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/1350486042000271638?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. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Fred Espen Benth, 2003. "On arbitrage-free pricing of weather derivatives based on fractional Brownian motion," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(4), pages 303-324.
    3. 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.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. 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.
    6. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    7. Dorje Brody & Joanna Syroka & Mihail Zervos, 2002. "Dynamical pricing of weather derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 2(3), pages 189-198.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. Fred Espen Benth & Lars Ekeland & Ragnar Hauge & BjøRn Fredrik Nielsen, 2003. "A note on arbitrage-free pricing of forward contracts in energy markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(4), pages 325-336.
    10. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68.
    Full references (including those not matched with items on IDEAS)

    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. Prabakaran, Sellamuthu & Garcia, Isabel C. & Mora, Jose U., 2020. "A temperature stochastic model for option pricing and its impacts on the electricity market," Economic Analysis and Policy, Elsevier, vol. 68(C), pages 58-77.
    2. 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, September.
    3. Fred Espen Benth & Jūratė Šaltytė Benth & Steen Koekebakker, 2007. "Putting a Price on Temperature," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 746-767, December.
    4. 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.
    5. Härdle, Wolfgang Karl & López-Cabrera, Brenda & Ritter, Matthias, 2012. "Forecast based pricing of weather derivatives," SFB 649 Discussion Papers 2012-027, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Borkowski, Bolesław & Krawiec, Monika & Shachmurove, Yochanan, 2013. "Impact of volatility estimation method on theoretical option values," Global Finance Journal, Elsevier, vol. 24(2), pages 119-128.
    7. 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).
    8. Boleslaw Borkowski & Monika Krawiec & Yochanan Shachmurove, 2013. "Modeling and Estimating Volatility of Options on Standard & Poor’s 500 Index," PIER Working Paper Archive 13-015, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    9. Adam Clements & A S Hurn & K A Lindsay, 2008. "Developing analytical distributions for temperature indices for the purposes of pricing temperature-based weather derivatives," NCER Working Paper Series 34, National Centre for Econometric Research.
    10. Rosella Castellano & Roy Cerqueti & Giulia Rotundo, 2020. "Exploring the financial risk of a temperature index: a fractional integrated approach," Annals of Operations Research, Springer, vol. 284(1), pages 225-242, January.
    11. Griffin, J.E. & Steel, M.F.J., 2006. "Inference with non-Gaussian Ornstein-Uhlenbeck processes for stochastic volatility," Journal of Econometrics, Elsevier, vol. 134(2), pages 605-644, October.
    12. Wolfgang Karl Härdle & Brenda López-Cabrera & Matthias Ritter, 2012. "Forecast based Pricing of Weather Derivatives," SFB 649 Discussion Papers SFB649DP2012-027, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. Zura Kakushadze & Juan Andrés Serur, 2018. "151 Trading Strategies," Springer Books, Springer, number 978-3-030-02792-6, June.
    14. Fred Benth & Wolfgang Karl Härdle & Brenda López Cabrera, 2009. "Pricing of Asian temperature risk," SFB 649 Discussion Papers SFB649DP2009-046, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    15. 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, September.
    16. 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.
    17. 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.
    18. 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.
    19. Lars Stentoft, 2008. "American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 540-582, Fall.
    20. Musshoff, Oliver & Hirschauer, Norbert, 2008. "Hedging von Mengenrisiken in der Landwirtschaft – Wie teuer dürfen „ineffektive“ Wetterderivate sein?," German Journal of Agricultural Economics, Humboldt-Universitaet zu Berlin, Department for Agricultural Economics, vol. 57(05), pages 1-12.

    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:12:y:2005:i:1:p:53-85. 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.