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A Fair Pricing Approach to Weather Derivatives

  • Eckhard Platen
  • Jason West

    ()

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

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File URL: http://hdl.handle.net/10.1007/s10690-005-4252-9
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Article provided by Springer in its journal Asia-Pacific Financial Markets.

Volume (Year): 11 (2004)
Issue (Month): 1 (March)
Pages: 23-53

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Handle: RePEc:kap:apfinm:v:11:y:2004:i:1:p:23-53
Contact details of provider: Web page: http://springerlink.metapress.com/link.asp?id=102851

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  1. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
  2. Eckhard Platen, 2003. "A Benchmark Framework for Risk Management," Research Paper Series 113, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Sean D. Campbell & Francis X. Diebold, 2003. "Weather Forecasting for Weather Derivatives," NBER Working Papers 10141, National Bureau of Economic Research, Inc.
  4. Eckhard Platen, 2003. "Modeling the Volatility and Expected Value of a Diversified World Index," Research Paper Series 103, Quantitative Finance Research Centre, University of Technology, Sydney.
  5. Takeaki Kariya, 2003. "Weather Risk Swap Valuation," KIER Working Papers 568, Kyoto University, Institute of Economic Research.
  6. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187.
  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. Eckhard Platen, 2003. "Diversified Portfolios in a Benchmark Framework," Research Paper Series 87, Quantitative Finance Research Centre, University of Technology, Sydney.
  9. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
  10. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
  11. 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 637-54, May-June.
  12. Eckhard Platen, 2003. "Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models," Research Paper Series 110, Quantitative Finance Research Centre, University of Technology, Sydney.
  13. 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.
  14. 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 857-85, June.
  15. 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.
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