In this study, we analyzed option pricing of rainfall derivatives based on stochastic daily rainfall model. We used Markov Chain Analogue Year model (MCAY) in order to describe occurrence process of daily rainfall. We have included the Analogue Year (AY) component in the Markov Chain (MC), which is a new component incorporated in this study and pricing rainfall derivatives. The inclusion of AY in the MC, provides excellent description of the occurrence process of daily rainfall. The amount of daily rainfall on wet days is obtained using Mixed Exponential distribution because it has the advantage of a better representation of extreme events. Combining the occurrence and amount model, we obtained Markov Chain Analogue Year Mixed Exponential model (MCAYMEM). Daily rainfall data from 2005 to 2017 were taken from Ethiopia National Meteorology Agency (ENMA) in order to assess the model performance. Based on the results of the daily rainfall models, we calculated an option price for different months. The price calculated using MCAYMEM gave an excellent result compared to the price calculated using MCMEM. This accuracy is mainly because of AY component included in the MC in the modeling of occurrence process.

In this paper, a Markov Chain Analogue Year model is used to describe the occurrence process of daily rainfall and the amount of daily rainfall on wet days is presented using Gamma, Exponential and mixed Exponential distributions. Combining the occurrence and the amount process models together, we developed Markov Chain Analogue Year Gamma model, Markov Chain Analogue Year Exponential model and Markov Chain Analogue Year Mixed Exponential model. The result shows that all the three models perform very well in the simulation of precipitation process in the study area and their performances are nearly the same with a slight difference. Using the results of these models, option prices for Teff and wheat crops for different months in their growing season are calculated. The calculated option price has an excellent accuracy with maximum absolute error of 0.54.instance rainfall fluctuation alone could contribute a loss of 2 billion USD in the sector [6]. In general, agriculture takes the first rank in the Ethiopian economy and it is extremely dependent on natural rainfall [4,51]. Therefore, modeling and pricing rainfall derivative is very important for the country in order to reduce such risks. This paper has two main objectives, the first objective is to present a daily rainfall model and the second objective is to use the daily rainfall model to obtain rainfall index, that is, cumulative rainfall (CR) and based on the CR, we calculate an option price for rainfall derivatives (for Teff and wheat crops). The paper is structured as follows: in Sect. 2 we have discussed materials and methods, model formulation, major crops and their response to water stress and description of pricing formula for rainfall derivatives, in Sect. 3 the obtained results are discussed under result and discussion, and finally in Sect. 4 we have made some concluding remarks.

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