In this thesis, we aim at modeling daily average temperature and pricing weather deriva tives based on the temperature in Ethiopia to hedge the risks associated with temperature fluctuations in the agricultural sector. For this purpose, we model the daily average tem perature data recorded in Ethiopia using a stochastic Ornstein-Uhlenbeck model where the random term is generated by the Lévy process. The daily average temperature data recorded in fifteen weather stations in Ethiopia are used to study the dynamics of tem perature. The nature of the historical data exhibits heavy tails and skewness. To capture these properties, we use the generalized hyperbolic distribution to model the dynamics of residuals. The method of least squared and maximum likelihood estimation (MLE) are employed to estimate the parameters of the models. To test the goodness of fit, we use the quantile-quantile (Q-Q) plot and the result shows that the generalized hyperbolic distri bution is by far better than the normal distribution to explain the dynamics of the random components of our model. The stochastic Ornstein-Uhlenbeck daily temperature model is used for simulating grow ing degree day(GDD) index. The Monte Carlo simulation technique is used to simulate temperature indices. We proposed normal distribution to model the simulated temperature indices. By applying the Escher transformation on normal distribution fitted to temper ature index, we calculate risk neutral prices for future and option temperature contracts. Since the weather derivatives market is an incomplete market, market price of risk is an important parameter to set fair price for both future and option contracts written on GDD indices. We have estimated this parameter from the historical temperature data by computing the GDD index for each particular month of the year, which is the main con tribution of this work. Then we used the estimated market price of risk to specify the vi risk-neutral probability measure Q for calculating future and option price. Finally, using the calculated value of market price of risk, we calculate future and option prices for Teff which is one of major cereal crops caltivated in Ethiopia, in its growing season specially in the months, July to November. These price values are more accurate than the value obtained assuming that, the market price of risk is zero. Therefore, our results show that the model performs well for modeling and pricing temperature derivatives to hedge the risk associated with temperature fluctuations under risk neutral measure. In nutshell, the main contributions of this thesis are: • We obtained an optimal model to capture the dynamics of temperature • We have calculated the future and option price • Uniquely to the related works in this field, we are able to calculate the market price of risk from the historical data, which is the main contribution of this thesis. This makes the work an international contribution and not bound to the Ethiopian case. • We have found temperature indices for particular places in Ethiopia • We indicated a hedging strategy for agricultural productivity risks which comes due to unfavorable weather condition. • For insurance companies in Ethiopia, this could be a new market.