A L\'evy-driven rainfall model with applications to futures pricing

摘要

We propose a parsimonious stochastic model for characterising thedistributional and temporal properties of rainfall. The model is based on anintegrated Ornstein-Uhlenbeck process driven by the Hougaard L\'evy process. Wederive properties of this process and propose an extended model whichgeneralises the Ornstein-Uhlenbeck process to the class of continuous-time ARMA(CARMA) processes. The model is illustrated by fitting it to empirical rainfalldata on both daily and hourly time scales. It is shown that the model issufficiently flexible to capture important features of the rainfall processacross locations and time scales. Finally we study an application to thepricing of rainfall derivatives which introduces the market price of risk viathe Esscher transform. We first give a result specifying the risk-neutralexpectation of a general moving average process. Then we illustrate the pricingmethod by calculating futures prices based on empirical daily rainfall data,where the rainfall process is specified by our model.