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A Fair Pricing Approach to Weather Derivatives

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Author Info

  • 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

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File URL: http://hdl.handle.net/10.1007/s10690-005-4252-9
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Bibliographic Info

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

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Web page: http://springerlink.metapress.com/link.asp?id=102851

Related research

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

References

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  1. 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.
  2. 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.
  3. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, 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.
  5. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
  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. 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.
  8. Eckhard Platen, 2003. "A Benchmark Framework for Risk Management," Research Paper Series 113, Quantitative Finance Research Centre, University of Technology, Sydney.
  9. Takeaki Kariya, 2003. "Weather Risk Swap Valuation," KIER Working Papers 568, Kyoto University, Institute of Economic Research.
  10. 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.
  11. Eckhard Platen, 2003. "Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models," Research Paper Series 110, Quantitative Finance Research Centre, University of Technology, Sydney.
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Citations

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Cited by:
  1. Wolfgang Härdle & Brenda López Cabrera, 2009. "Implied Market Price of Weather Risk," SFB 649 Discussion Papers SFB649DP2009-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  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. Hélène Hamisultane, 2008. "Which Method for Pricing Weather Derivatives ?," Working Papers halshs-00355856, HAL.

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