IDEAS home Printed from https://ideas.repec.org/a/gam/jijfss/v5y2017i4p23-d115840.html
   My bibliography  Save this article

A Dynamic Programming Approach for Pricing Weather Derivatives under Issuer Default Risk

Author

Listed:
  • Wolfgang Karl Härdle

    (Ladislaus von Bortkiewicz Chair of Statistics, School of Business and Economics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
    Sim Kee Boon Institute for Financial Economics, Singapore Management University, 90 Stamford Road, 6th Level, School of Economics, Singapore 178903, Singapore
    Current address: Ladislaus von Bortkiewicz Chair of Statistics, School of Business and Economics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany.
    These authors contributed equally to this work.)

  • Maria Osipenko

    (Ladislaus von Bortkiewicz Chair of Statistics, School of Business and Economics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
    These authors contributed equally to this work.)

Abstract

Weather derivatives are contingent claims with payoff based on a pre-specified weather index. Firms exposed to weather risk can transfer it to financial markets via weather derivatives. We develop a utility-based model for pricing baskets of weather derivatives under default risk on the issuer side in over-the-counter markets. In our model, agents maximise the expected utility of their terminal wealth, while they dynamically rebalance their weather portfolios over a finite investment horizon. Using dynamic programming approach, we obtain semi-closed forms for the equilibrium prices of weather derivatives and for the optimal strategies of the agents. We give an example on how to price rainfall derivatives on selected stations in China in the universe of a financial investor and a weather exposed crop insurer.

Suggested Citation

  • Wolfgang Karl Härdle & Maria Osipenko, 2017. "A Dynamic Programming Approach for Pricing Weather Derivatives under Issuer Default Risk," IJFS, MDPI, vol. 5(4), pages 1-18, October.
    • Handle: RePEc:gam:jijfss:v:5:y:2017:i:4:p:23-:d:115840
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7072/5/4/23/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7072/5/4/23/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Linda L. Golden & Mulong Wang & Chuanhou Yang, 2007. "Handling Weather Related Risks Through the Financial Markets: Considerations of Credit Risk, Basis Risk, and Hedging," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(2), pages 319-346, June.
    3. Ulrich Horst & Matthias Müller, 2007. "On the Spanning Property of Risk Bonds Priced by Equilibrium," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 784-807, November.
    4. Allen, Franklin & Postlewaite, Andrew, 1984. "Rational Expectations and the Measurement of a Stock's Elasticity of Demand," Journal of Finance, American Finance Association, vol. 39(4), pages 1119-1125, September.
    5. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409, World Scientific Publishing Co. Pte. Ltd..
    6. 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.
    7. 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.
    8. Wu, Yang-Che & Chung, San-Lin, 2010. "Catastrophe risk management with counterparty risk using alternative instruments," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 234-245, October.
    9. Hull, John & White, Alan, 1995. "The impact of default risk on the prices of options and other derivative securities," Journal of Banking & Finance, Elsevier, vol. 19(2), pages 299-322, May.
    10. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    11. 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.
    12. 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.
    13. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    14. 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.
    15. World Bank, 2007. "China : Innovations in Agricultural Insurance," World Bank Publications - Reports 12401, The World Bank Group.
    16. Calum G. Turvey & Rong Kong, 2010. "Weather risk and the viability of weather insurance in China's Gansu, Shaanxi, and Henan provinces," China Agricultural Economic Review, Emerald Group Publishing Limited, vol. 2(1), pages 5-24, February.
    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. CMaria Osipenko & Wolfgang Karl Härdle, 2017. "Dynamic Valuation of Weather Derivatives under Default Risk," SFB 649 Discussion Papers SFB649DP2017-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    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, December.
    3. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    4. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    5. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    6. 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.
    7. Aur'elien Alfonsi & Nerea Vadillo, 2023. "Risk valuation of quanto derivatives on temperature and electricity," Papers 2310.07692, arXiv.org.
    8. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011.
    9. Tong, Zhigang & Liu, Allen, 2021. "A censored Ornstein–Uhlenbeck process for rainfall modeling and derivatives pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    10. Musshoff, Oliver & Odening, Martin & Xu, Wei, 2005. "Zur Bewertung von Wetterderivaten als innovative Risikomanagementinstrumente in der Landwirtschaft," German Journal of Agricultural Economics, Humboldt-Universitaet zu Berlin, Department for Agricultural Economics, vol. 54(04), pages 1-13.
    11. Szu-Lang Liao & Hsing-Hua Huang, 2005. "Pricing Black-Scholes options with correlated interest rate risk and credit risk: an extension," Quantitative Finance, Taylor & Francis Journals, vol. 5(5), pages 443-457.
    12. 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.
    13. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.
    14. 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.
    15. Jarrow, Robert A. & Turnbull, Stuart M., 2000. "The intersection of market and credit risk," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 271-299, January.
    16. Ragnhild Noven & Almut Veraart & Axel Gandy, 2015. "A Lévy-driven rainfall model with applications to futures pricing," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(4), pages 403-432, October.
    17. Chen, Bin & Hong, Yongmiao, 2012. "Testing For The Markov Property In Time Series," Econometric Theory, Cambridge University Press, vol. 28(1), pages 130-178, February.
    18. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    19. Yeny E. Rodríguez & Miguel A. Pérez-Uribe & Javier Contreras, 2021. "Wind Put Barrier Options Pricing Based on the Nordix Index," Energies, MDPI, vol. 14(4), pages 1-14, February.
    20. 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.

    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:5:y:2017:i:4:p:23-:d:115840. 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.