Markov Chain Analogue Year Daily Rainfall Models and Pricing Rainfall Derivatives

SHIBABAW, NURILIGN

dc.contributor.author	SHIBABAW, NURILIGN
dc.date.accessioned	2021-11-06T05:34:53Z
dc.date.available	2021-11-06T05:34:53Z
dc.date.issued	2021-11-06
dc.identifier.uri	http://ir.bdu.edu.et/handle/123456789/12898
dc.description.abstract	In this thesis, we aim at modeling daily rainfall and pricing rainfall derivatives in Ethiopia. To this end, the standardized two part modeling approach which is known as "occurrence amount process" model is used to model daily rainfall in Ethiopia. A daily rainfall con sists of two components: the occurrence process of daily rainfall and the amount of rain fall on wet days. Therefore, these two components of the daily rainfall are modeled sepa rately. In order to model the occurrence process, we used Markov chain(MC) and Markov chain analogue year(MCAY) model, that is Markov chain with the AY component which is a new component and the main contribution of this dissertation. The performance of these two models are compared and the result shows that the MCAY model describes the occurrence process in an excellent way compared to Markov chain (MC without the AY component). In the second part of the model, that is, in the amount of the daily rainfall modeling part, four different nonnegative continuous probability distributions are used: exponen tial, mixed exponential, gamma and Weibull distributions. The parameters of these distri butions are estimated using maximum likelihood estimation (MLE). Then by combing the two component models (the occurrence and amount model), we developed four different stochastic daily rainfall models: Markov chain analogue year exponential model(MCAYEM), Markov chain analogue year mixed exponential model(MCAYMEM), Markov chain ana logue year gamma model(MCAYGM) and Markov chain analogue year Weibull model (MCAYWBM). The performance of these models are assessed by taking daily rainfall data from 21 weather stations from different parts of Ethiopia. The result revealed that the analoguev year(AY) component included in this study show great effect on describing the occur rence process of daily rainfall. Also it is observed that all the four distributions in combination with the MCAY that is, MCAYEM, MCAYMEM, MCAYGM and MCAY WBM have nearly the same performance with only slight difference between them. Since MCAYMEM has slightly better overall performance compared to the other three models, the MCAYMEM is used to simulate 10,000 paths via Monte Carlo simulation to obtain rainfall index. Then the simulated index is fitted to Gamma distribution and transformed using Esscher transform to obtain risk neutral price. Finally, we calculate option price for Teff and wheat crops in their growing season because these crops are among the most common crops in production and area coverage in Ethiopia	en_US
dc.language.iso	en_US	en_US
dc.subject	Mathematics	en_US
dc.title	Markov Chain Analogue Year Daily Rainfall Models and Pricing Rainfall Derivatives	en_US
dc.type	Thesis	en_US