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A Fair Pricing Approach to Weather Derivatives

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  • Eckhard Platen
  • Jason West

Abstract

This paper proposes a consistent approach to the pricing of weather derivatives. Since weather derivatives are traded in an incomplete market setting, standard hedging based pricing methods cannot be applied. The growth optimal portfolio, which is interpreted as a world stock index, is used as a benchmark or numeraire such that all benchmarked derivative price processes are martingales. No measure transformation is needed for the proposed fair pricing. For weather derivative payoffs that are independent of 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. The fair prices of some particular weather derivatives are derived using historical and Gaussian residuals. The question of weather risk as diversifiable risk is also discussed. Copyright Springer Science + Business Media, Inc. 2004

Suggested Citation

  • Eckhard Platen & Jason West, 2004. "A Fair Pricing Approach to Weather Derivatives," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 23-53, March.
    • Handle: RePEc:kap:apfinm:v:11:y:2004:i:1:p:23-53
    DOI: 10.1007/s10690-005-4252-9
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    References listed on IDEAS

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    1. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
    2. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187, July.
    3. 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.
    4. 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, October.
    5. 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.
    6. 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.
    7. Bühlmann, Hans & Platen, Eckhard, 2003. "A Discrete Time Benchmark Approach for Insurance and Finance," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 153-172, November.
    8. Karyl Leggio & Donald Lien, 2002. "Hedging gas bills with weather derivatives," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 26(1), pages 88-100, March.
    9. Takeaki Kariya, 2003. "Weather Risk Swap Valuation," KIER Working Papers 568, Kyoto University, Institute of Economic Research.
    10. Eckhard Platen, 2004. "A Benchmark Framework for Risk Management," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 15, pages 305-335, World Scientific Publishing Co. Pte. Ltd..
    11. 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..
    12. 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.
    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. Ralf Korn & Manfred Schäl, 1999. "On value preserving and growth optimal portfolios," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 189-218, October.
    15. Eckhard Platen, 2003. "Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models," Research Paper Series 110, Quantitative Finance Research Centre, University of Technology, Sydney.
    16. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
    17. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
    18. 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.
    19. Eckhard Platen, 2003. "Diversified Portfolios in a Benchmark Framework," Research Paper Series 87, Quantitative Finance Research Centre, University of Technology, Sydney.
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    More about this item

    Keywords

    actuarial pricing; benchmark approach; fair pricing; growth optimal portfolio; weather derivatives;
    All these keywords.

    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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