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Fair Pricing of Weather Derivatives

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Abstract

This paper proposes a consistent benchmark approach to price weather derivatives. The growth optimal portfolio to price weather derivatives. The growth optimal portfolio is used as numeraire such that all benchmarked fair price processes are martingales. No measure transformation is needed for fair pricing. Since weather derivatives are traded in an incomplete market setting, standard hedging based pricing methods cannot be applied. For weather derivative payoffs that are independent from the value of the growth optimal portfolio it is shown that the classical actuarial pricing methodology is a particular case of the fair pricing concept. A discrete time model is constructed to approximate historical weather characteristics assuming Gaussian residuals. For particular weather derivatives their fair prices are derived.

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  • Eckhard Platen & Jason West, 2003. "Fair Pricing of Weather Derivatives," Research Paper Series 106, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:106
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    References listed on IDEAS

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    1. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187.
    2. Eckhard Platen, 2004. "A Benchmark Framework for Risk Management," World Scientific Book Chapters,in: Stochastic Processes And Applications To Mathematical Finance, chapter 15, pages 305-335 World Scientific Publishing Co. Pte. Ltd..
    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. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187.
    5. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Fama, Eugene F & MacBeth, James D, 1974. "Long-Term Growth in a Short-Term Market," Journal of Finance, American Finance Association, vol. 29(3), pages 857-885, June.
    7. Hans Buhlmann & Eckhard Platen, 2002. "A Discrete Time Benchmark Approach for Finance and Insurance," Research Paper Series 74, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Takeaki Kariya, 2003. "Weather Risk Swap Valuation," KIER Working Papers 568, Kyoto University, Institute of Economic Research.
    9. repec:wsi:ijtafx:v:07:y:2004:i:04:n:s0219024904002499 is not listed on IDEAS
    10. Eckhard Platen, 2003. "Diversified Portfolios in a Benchmark Framework," Research Paper Series 87, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
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    13. Eckhard Platen, 2004. "Modeling The Volatility And Expected Value Of A Diversified World Index," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 511-529.
    14. Eckhard Platen, 2003. "Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models," Research Paper Series 110, Quantitative Finance Research Centre, University of Technology, Sydney.
    15. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
    16. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 385-413.
    17. I. Bajeux-Besnainou & R. Portait, 1997. "The numeraire portfolio: a new perspective on financial theory," The European Journal of Finance, Taylor & Francis Journals, vol. 3(4), pages 291-309.
    18. 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.
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    Cited by:

    1. 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.
    2. Lee, Yongheon & Oren, Shmuel S., 2009. "An equilibrium pricing model for weather derivatives in a multi-commodity setting," Energy Economics, Elsevier, vol. 31(5), pages 702-713, September.
    3. Eckhard Platen, 2004. "A Benchmark Framework for Risk Management," World Scientific Book Chapters,in: Stochastic Processes And Applications To Mathematical Finance, chapter 15, pages 305-335 World Scientific Publishing Co. Pte. Ltd..
    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. 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.
    6. Adam Clements & A S Hurn & K A Lindsay, 2008. "Estimating the Payoffs of Temperature-based Weather Derivatives," NCER Working Paper Series 33, National Centre for Econometric Research.
    7. 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.
    8. Hélène Hamisultane, 2006. "Pricing the Weather Derivatives in the Presence of Long Memory in Temperatures," Working Papers halshs-00079197, HAL.
    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. Yuji Yamada, 2008. "Optimal Hedging of Prediction Errors Using Prediction Errors," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 15(1), pages 67-95, March.
    11. Wolfgang Härdle & Brenda López Cabrera, 2009. "Implied Market Price of Weather Risk," SFB 649 Discussion Papers SFB649DP2009-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    12. FRED ESPEN BENTH & JŪRATĖ SALTYTĖ 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.
    13. Hélène Hamisultane, 2008. "Which Method for Pricing Weather Derivatives ?," Working Papers halshs-00355856, HAL.
    14. L. Kermiche & N. Vuillermet, 2016. "Weather derivatives structuring and pricing: a sustainable agricultural approach in Africa," Applied Economics, Taylor & Francis Journals, vol. 48(2), pages 165-177, January.
    15. Svec, J. & Stevenson, M., 2007. "Modelling and forecasting temperature based weather derivatives," Global Finance Journal, Elsevier, vol. 18(2), pages 185-204.

    More about this item

    Keywords

    weather derivatives; benchmark approach; growth optimal portfolio; fair pricing; actuarial pricing;

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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