The performance of many firms are exposed to the changes in weather. The industry sectors exposed to 'weather risk' are basic materials, consumer durables and agricultural industries. Amongst these the basic materials has mainly triggered the demand for the weather derivatives market and the rapid growth in the weather risk assessment industry. With this as the backdrop, this book formulates a pricing model for the weather derivatives, whose payoffs depend on surface air temperature. Daily temperature data for the last thirty years is closely analyzed for four cities in U.K. to model a temperature process which captures the daily temperature fluctuations including the seasonal patterns and the year-on- year up-ward trend behaviour of the temperature.This work further evaluates an arbitrage-free option pricing using a Gaussian Ornstein-Uhlenbeck model. Keeping in mind that temperature, the underlying variable of the weather derivative, is non-tradable we consider a risk premium estimator to find the price of a weather derivatives contract. Further, the book provides results based on these models as well as based on Monte Carlo Simulations.