Abstract

We consider the problem of pricing a derivative contract written on precipitation at a specific location during a given period of time. We propose a jump Markov process model for the stochastic dynamics of the underlying precipitation. Our model is based on pulse Poisson process models widely used in hydrology. We develop maximum likelihood parameter estimation procedures to fit our model to rainfall data. In order to price derivatives, we assume the existence of a traded asset whose price dynamics are influenced by the precipitation at the location in question, and we rely on the utility indifference approach. Two utility functions are considered: exponential and power utility. We derive explicit solutions for the exponential and bounds for the power utility. Finally, we apply our model fitting and pricing techniques to a sample rainfall contract in Norway.

Original languageEnglish (US)
Pages (from-to)959-988
Number of pages30
JournalInternational Journal of Theoretical and Applied Finance
Volume8
Issue number7
DOIs
StatePublished - Nov 1 2005

All Science Journal Classification (ASJC) codes

  • Finance
  • Economics, Econometrics and Finance(all)

Keywords

  • Jump Markov processes
  • Maximum likelihood estimation
  • Precipitation modeling
  • Utility indifference pricing
  • Weather derivatives

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