This paper extended the Cao-Wei (2004, JFM) model to construct a theoretical model for pricing weather derivatives in two significant ways. One adopted a time series model developed by Campbell and Diebold (2005, JASA) to describe the dynamics of temperature. The advantage of using Campbell and Diebold's time series model to describe the temperature dynamics is that it can not only take the conditional mean of temperature coming from trend, seasonal, and cyclical components but also allow for the conditional variance dynamics. The other purpose of this paper is to use an extended power utility function, instead of Cao and Wei's constant proportional risk aversion (CPRA) utility function. The extended power utility function could exhibit decreasing, constant, and increasing relative risk aversion. Eventually, we find that the prices of weather derivatives can be determined by weather conditions, discount factors, and forward premiums. Additionally, these sources have close relations with some risk aversion parameters. Furthermore, the results are consistent with Cao and Wei's condition under some specific parameter assumptions.
