IDEAS home Printed from https://ideas.repec.org/a/gam/jijfss/v7y2019i3p35-d243312.html
   My bibliography  Save this article

Pricing Basket Weather Derivatives on Rainfall and Temperature Processes

Author

Listed:
  • Nelson Christopher Dzupire

    (Mathematics Department, Pan African University Institute of Basic Sciences, Technology, and Innovation, Juja, Nairobi 00200, Kenya)

  • Philip Ngare

    (Mathematics Department, Pan African University Institute of Basic Sciences, Technology, and Innovation, Juja, Nairobi 00200, Kenya
    Department Actuarial Science, University of Nairobi, Nairobi 00100, Kenya)

  • Leo Odongo

    (Mathematics Department, Pan African University Institute of Basic Sciences, Technology, and Innovation, Juja, Nairobi 00200, Kenya
    Department of Statistics and Actuarial Science, Kenyatta University, Nairobi 00100, Kenya)

Abstract

This paper follows an incomplete market pricing approach to analyze the evaluation of weather derivatives and the viability of a weather derivatives market in terms of hedging. A utility indifference method is developed for the specification of indifference prices for the seller and buyer of a basket of weather derivatives written on rainfall and temperature. The agent’s risk preference is described by an exponential utility function and the prices are derived by dynamic programming principles and corresponding Hamilton Jacobi-Bellman equations from the stochastic optimal control problems. It is found the indifference measure is equal to the physical measure as there is no correlation between the capital market and weather. The fair price of the derivative should be greater than the seller’s indifference price and less than the buyer’s indifference price for market viability and no arbitrage opportunities.

Suggested Citation

  • Nelson Christopher Dzupire & Philip Ngare & Leo Odongo, 2019. "Pricing Basket Weather Derivatives on Rainfall and Temperature Processes," IJFS, MDPI, vol. 7(3), pages 1-14, June.
    • Handle: RePEc:gam:jijfss:v:7:y:2019:i:3:p:35-:d:243312
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7072/7/3/35/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7072/7/3/35/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. López Cabrera, Brenda & Odening, Martin & Ritter, Matthias, 2013. "Pricing rainfall derivatives at the CME," SFB 649 Discussion Papers 2013-005, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    2. 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.
    3. Ernst Eberlein & Jean Jacod, 1997. "On the range of options prices (*)," Finance and Stochastics, Springer, vol. 1(2), pages 131-140.
    4. Cong, Rong-Gang & Brady, Mark, 2012. "The Interdependence between Rainfall and Temperature: Copula Analyses," MPRA Paper 112149, University Library of Munich, Germany.
    5. Xu, Wei & Odening, Martin & Musshoff, Oliver, 2007. "Indifference Pricing of Weather Insurance," 101st Seminar, July 5-6, 2007, Berlin Germany 9267, European Association of Agricultural Economists.
    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. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    8. René Carmona & Pavel Diko, 2005. "Pricing Precipitation Based Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(07), pages 959-988.
    9. Vedenov, Dmitry V. & Barnett, Barry J., 2004. "Efficiency of Weather Derivatives as Primary Crop Insurance Instruments," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 29(3), pages 1-17, December.
    10. 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.
    11. Calum G. Turvey, 2001. "Weather Derivatives for Specific Event Risks in Agriculture," Review of Agricultural Economics, Agricultural and Applied Economics Association, vol. 23(2), pages 333-351.
    12. Deepak K. Ray & James S. Gerber & Graham K. MacDonald & Paul C. West, 2015. "Climate variation explains a third of global crop yield variability," Nature Communications, Nature, vol. 6(1), pages 1-9, May.
    13. Marek Musiela & Thaleia Zariphopoulou, 2004. "An example of indifference prices under exponential preferences," Finance and Stochastics, Springer, vol. 8(2), pages 229-239, May.
    14. Hertzler, Greg, 2003. "A Stochastic Differential Equation for Modeling the “Classical” Probability Distributions," 2003 Conference (47th), February 12-14, 2003, Fremantle, Australia 57891, Australian Agricultural and Resource Economics Society.
    15. Patrick Brockett & Linda Goldens & Min-Ming Wen & Charles Yang, 2009. "Pricing Weather Derivatives Using the Indifference Pricing Approach," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(3), pages 303-315.
    16. Syroka, Joanna & Nucifora, Antonio, 2010. "National drought insurance for Malawi," Policy Research Working Paper Series 5169, The World Bank.
    17. Martin Odening & Oliver Musshoff & Wei Xu, 2007. "Analysis of rainfall derivatives using daily precipitation models: opportunities and pitfalls," Agricultural Finance Review, Emerald Group Publishing Limited, vol. 67(1), pages 135-156, May.
    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. Andrea Martínez Salgueiro & Maria-Antonia Tarrazon-Rodon, 2021. "Weather derivatives to mitigate meteorological risks in tourism management: An empirical application to celebrations of Comunidad Valenciana (Spain)," Tourism Economics, , vol. 27(4), pages 591-613, June.
    2. 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.
    3. 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.
    4. Andrea Martínez Salgueiro & Maria-Antonia Tarrazon-Rodon, 2020. "Approaching rainfall-based weather derivatives pricing and operational challenges," Review of Derivatives Research, Springer, vol. 23(2), pages 163-190, July.
    5. Bucheli, Janic & Dalhaus, Tobias & Finger, Robert, 2022. "Temperature effects on crop yields in heat index insurance," Food Policy, Elsevier, vol. 107(C).
    6. 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.
    7. 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.
    8. Sun, Baojing & van Kooten, G. Cornelis, 2014. "Financial Weather Options for Crop Production," Working Papers 164323, University of Victoria, Resource Economics and Policy.
    9. Baojing Sun & Changhao Guo & G. Cornelis van Kooten, 2013. "Weather Derivatives and Crop Insurance in China," Working Papers 2013-02, University of Victoria, Department of Economics, Resource Economics and Policy Analysis Research Group.
    10. Markus Stowasser, 2011. "Modelling rain risk: a multi-order Markov chain model approach," Journal of Risk Finance, Emerald Group Publishing, vol. 13(1), pages 45-60, December.
    11. Juárez-Torres, Miriam & Sánchez-Aragón, Leonardo & Vedenov, Dmitry, 2017. "Weather Derivatives and Water Management in Developing Countries: An Application for an Irrigation District in Central Mexico," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 42(2), May.
    12. Sun, Baojing, 2017. "Financial Weather Derivatives for Corn Production in Northeastern China: Modelling the underlying Weather Index," Working Papers 263197, University of Victoria, Resource Economics and Policy.
    13. López Cabrera, Brenda & Odening, Martin & Ritter, Matthias, 2013. "Pricing rainfall derivatives at the CME," SFB 649 Discussion Papers 2013-005, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    14. Xu, Wei & Odening, Martin & Musshoff, Oliver, 2007. "Indifference Pricing of Weather Insurance," 101st Seminar, July 5-6, 2007, Berlin Germany 9267, European Association of Agricultural Economists.
    15. Mußhoff, O. & Odenin, M. & Wei, X., 2007. "Zur Quantifizierung des Basisrisikos von Wetterderivaten," Proceedings “Schriften der Gesellschaft für Wirtschafts- und Sozialwissenschaften des Landbaues e.V.”, German Association of Agricultural Economists (GEWISOLA), vol. 42, March.
    16. Martínez-Salgueiro, Andrea & Tarrazón-Rodón, María-Antonia, 2020. "Is diversification effective in reducing the systemic risk implied by a market for weather index-based insurance in Spain?," MPRA Paper 119924, University Library of Munich, Germany, revised 19 May 2021.
    17. repec:hum:wpaper:sfb649dp2013-005 is not listed on IDEAS
    18. Doms, Juliane, 2017. "Put, call or strangle? About the challenges in designing weather index insurances to hedge performance risk in agriculture," 57th Annual Conference, Weihenstephan, Germany, September 13-15, 2017 261990, German Association of Agricultural Economists (GEWISOLA).
    19. Sun, Baojing, 2017. "Financial Weather Derivatives for Corn Production in Northeastern China: Modelling the Underlying Weather Index," Working Papers 257083, University of Victoria, Resource Economics and Policy.
    20. López Cabrera, Brenda & Odening, Martin & Ritter, Matthias, 2013. "Pricing rainfall futures at the CME," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4286-4298.
    21. Baojing Sun, 2017. "Financial Weather Derivatives for Corn Production in Northeastern China: Modelling the underlying Weather Index," Working Papers 2017-05, University of Victoria, Department of Economics, Resource Economics and Policy Analysis Research Group.

    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:gam:jijfss:v:7:y:2019:i:3:p:35-:d:243312. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.