  We propose a parsimonious stochastic model for characterising the
distributional and temporal properties of rainfall. The model is based on an
integrated Ornstein-Uhlenbeck process driven by the Hougaard L\'evy process. We
derive properties of this process and propose an extended model which
generalises the Ornstein-Uhlenbeck process to the class of continuous-time ARMA
(CARMA) processes. The model is illustrated by fitting it to empirical rainfall
data on both daily and hourly time scales. It is shown that the model is
sufficiently flexible to capture important features of the rainfall process
across locations and time scales. Finally we study an application to the
pricing of rainfall derivatives which introduces the market price of risk via
the Esscher transform. We first give a result specifying the risk-neutral
expectation of a general moving average process. Then we illustrate the pricing
method by calculating futures prices based on empirical daily rainfall data,
where the rainfall process is specified by our model.
