In this paper, we develop a pricing model for weather derivatives at a single location and multiple locations. In the first model, a Lévy regime-switching temperature model for a single location is used to price futures written on cumulative average temperature and growing degree-days indices at a single location. To allow analytical pricing for futures on temperature basket, an [Formula: see text]-dimension regime-switching temperature model whose driving noise is captured by a Brownian motion is developed. The correlation between the driving noise in each regime is assumed to be a function of the space between the different farming locations and increases with decreasing space. The temperature basket index assigns a weight to each location that is exposed to risk. However, a location with a higher risk is assigned a larger weight and vice versa. By assuming that the regimes are independent to each other, the future is calculated for each regime model. The final futures price is calculated using the weighted sum of the individual regimes. These pricing models can be applied in the future markets to price weather derivatives for the agricultural sector. Research on spatial-temporal pricing model is vital to the development of the weather derivatives market, as investors are more vulnerable to temperature risk over different farming locations as compared to single location.
A multi-period equilibrium pricing model of weather derivatives