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A Fair Pricing Approach to Weather Derivatives

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Author Info
Eckhard Platen
Jason West ()

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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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Publisher 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

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

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341. [Downloadable!] (restricted)
  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. [Downloadable!]
  3. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Blackwell Publishing, vol. 11(4), pages 385-413. [Downloadable!] (restricted)
  4. Takeaki Kariya, 2003. "Weather Risk Swap Valuation," KIER Working Papers 568, Kyoto University, Institute of Economic Research.
  5. Eckhard Platen, 2003. "Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models," Research Paper Series 110, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  6. N. Hofmann & E. Platen & M. Schweizer, 1992. "Option Pricing under Incompleteness and Stochastic Volatility," Discussion Paper Serie B 209, University of Bonn, Germany.
  7. I. Bajeux-Besnainou, R. Portait, 1997. "The numeraire portfolio: a new perspective on financial theory," European Journal of Finance, Taylor and Francis Journals, vol. 3(4), pages 291-309, December. [Downloadable!] (restricted)
  8. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring. [Downloadable!] (restricted)
  9. 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. [Downloadable!]
  10. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  11. Eckhard Platen, 2003. "A Benchmark Framework for Risk Management," Research Paper Series 113, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  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 637-54, May-June. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Hélène Hamisultane, 2008. "Which Method for Pricing Weather Derivatives ?," Working Papers halshs-00355856_v1, HAL. [Downloadable!]
  2. Wolfgang Härdle & Brenda López Cabrera, 2009. "Implied Market Price of Weather Risk," SFB 649 Discussion Papers SFB649DP2009-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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