Wind time series forecasting with underlying semi-Markov model: an application to weather derivatives

Forecasting wind speed and direction is a challenging issue in the fi eld of meteorological research. This topic appears to be of great importance in other research areas. For instance, quantitative fi nance may be involved due to the recent development of wind insurance risk contracts. In this paper we set up a stochastic model able to determine the dynamic evolution of wind direction and speed at a given location. The wind direction is modeled through a nonparametric homogeneous semi-Markov process where the states are the eight main sectors of the wind rose. The wind speed is then modeled for each state by an empirical distribution. The main features of the model are estimated thanks to a database containing 30 years’ wind characteristics for Boston city on an hourly basis. The model is then tested with a Monte Carlo simulation and we compare then the results with the empirical data. Finally, we use the results for the pricing of a wind risk contract issued for a wind farm