PRICING PRECIPITATION BASED DERIVATIVES
- 21 November 2005
- journal article
- Published by World Scientific Pub Co Pte Ltd in International Journal of Theoretical and Applied Finance
- Vol. 8 (7), 959-988
- https://doi.org/10.1142/s0219024905003311
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.Keywords
This publication has 18 references indexed in Scilit:
- VALUATION OF CLAIMS ON NONTRADED ASSETS USING UTILITY MAXIMIZATIONMathematical Finance, 2002
- Rainfall modelling using Poisson-cluster processes: a review of developmentsStochastic Environmental Research and Risk Assessment, 2000
- The weather generation game: a review of stochastic weather modelsProgress in Physical Geography: Earth and Environment, 1999
- Optimization of consumption with labor incomeFinance and Stochastics, 1998
- Hedging in incomplete markets with HARA utilityJournal of Economic Dynamics and Control, 1997
- A switching poisson process model for high concentrations in short-range atmospheric dispersionAtmospheric Environment, 1997
- A generalized point process model for rainfallProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1994
- A point process model for rainfall: further developmentsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1988
- Some models for rainfall based on stochastic point processesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1987
- Numerical weather predictionProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1986