IDEAS home Printed from https://ideas.repec.org/a/wly/jnlamp/v2018y2018i1n2789412.html

Stability and Complexity Analysis of Temperature Index Model Considering Stochastic Perturbation

Author

Listed:
  • Jing Wang

Abstract

A temperature index model with delay and stochastic perturbation is constructed in this paper. It explores the influence of parameters and stochastic factors on the stability and complexity of the model. Based on historical temperature data of four cities of Anhui Province in China, the temperature periodic variation trends of approximately sinusoidal curves of four cities are given, respectively. In addition, we analyze the existence conditions of the local stability of the temperature index model without stochastic term and estimate its parameters by using the same historical data of the four cities, respectively. The numerical simulation results of the four cities are basically consistent with the descriptions of their historical temperature data, which proves that the temperature index model constructed has good fitting degree. It also shows that unreasonable delay parameter can make the model lose stability and improve the complexity. Stochastic factors do not usually change the trend in temperature, but they can cause high frequency fluctuations in the process of temperature evolution. Stability control is successfully realized for unstable systems by the variable feedback control method. The trend of temperature changes in Anhui Province is deduced by analyzing four typical cities.

Suggested Citation

  • Jing Wang, 2018. "Stability and Complexity Analysis of Temperature Index Model Considering Stochastic Perturbation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2018(1).
    • Handle: RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:2789412
    DOI: 10.1155/2018/2789412
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2018/2789412
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2018/2789412?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
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Balint, T. & Lamperti, F. & Mandel, A. & Napoletano, M. & Roventini, A. & Sapio, A., 2017. "Complexity and the Economics of Climate Change: A Survey and a Look Forward," Ecological Economics, Elsevier, vol. 138(C), pages 252-265.
    3. Mihailović, Dragutin & Kostić, Vladimir & Mimić, Gordan & Cvetković, Ljiljana, 2015. "Stability analysis of turbulent heat exchange over the heterogeneous environmental interface in climate models," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 79-90.
    4. 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.
    5. Melanie Cao & Jason Wei, 2004. "Weather derivatives valuation and market price of weather risk," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 24(11), pages 1065-1089, November.
    6. Dorje Brody & Joanna Syroka & Mihail Zervos, 2002. "Dynamical pricing of weather derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 2(3), pages 189-198.
    7. 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.
    8. repec:spo:wpmain:info:hdl:2441/1nlv566svi86iqtetenms15tc4 is not listed on IDEAS
    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. 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.
    2. Gülpınar, Nalân & Çanakoḡlu, Ethem, 2017. "Robust portfolio selection problem under temperature uncertainty," European Journal of Operational Research, Elsevier, vol. 256(2), pages 500-523.
    3. 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.
    4. 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.
    5. 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.
    6. 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).
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Alessio Giorgini & Rogemar S. Mamon & Marianito R. Rodrigo, 2021. "A Stochastic Harmonic Oscillator Temperature Model for the Valuation of Weather Derivatives," Mathematics, MDPI, vol. 9(22), pages 1-15, November.
    13. 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.
    14. Lunina, Veronika, 2016. "Joint Modelling of Power Price, Temperature, and Hydrological Balance with a View towards Scenario Analysis," Working Papers 2016:30, Lund University, Department of Economics.
    15. Zura Kakushadze & Juan Andrés Serur, 2018. "151 Trading Strategies," Springer Books, Springer, number 978-3-030-02792-6, October.
    16. Romain Biard & Christophette Blanchet-Scalliet & Anne Eyraud-Loisel & Stéphane Loisel, 2013. "Impact of Climate Change on Heat Wave Risk," Risks, MDPI, vol. 1(3), pages 1-16, December.
    17. Asante Gyamerah, Samuel & Ngare, Philip & Ikpe, Dennis, 2018. "A Levy Regime-Switching Temperature Dynamics Model for Weather Derivatives," MPRA Paper 89680, University Library of Munich, Germany, revised 10 Jul 2018.
    18. 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.
    19. Dupuis, Debbie J., 2011. "Forecasting temperature to price CME temperature derivatives," International Journal of Forecasting, Elsevier, vol. 27(2), pages 602-618.
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnlamp:v:2018:y:2018:i:1:n:2789412. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/3197 .

    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.