Rainfall derivatives pricing with underlying semi-Markov model for precipitation occurrences

Weather derivatives represent a new and particular kind of contingent claim which shares a specific underlying weather index. These derivatives are written for different temperature indices, hurricanes, frost, snowfall and rainfall, and they are available for several cities. Our paper focuses on rainfall derivatives. In order to price this kind of derivatives, we have to model daily rainfall sequences at a specific location. For this purpose, we adopt a non-homogeneous parametric semi-Markov model to describe the rainfall occurrences, and a mixture of exponential distributions for rainfall amounts. The underlying Markov process has the obvious two states: dry and wet. In addition, dry and wet sequences are estimated by using best-fitting techniques. The model parameters are determined thanks to classical log-likelihood maximization. We finally price some rainfall contracts issued by the Chicago Mercantile Exchange through Monte Carlo simulation. The numerical applications and the parameter estimations are carried out using real data.