Markov Chain Analogue Year Daily Rainfall Model and Pricing of Rainfall Derivatives
الموضوعات : فصلنامه ریاضی
Tesfahun Berhane
1
(Department of Mathematics, Bahir Dar University, Bahir Dar, Ethiopia.)
Nurilign Shibabaw
2
(Department of Mathematics, Bahir Dar University, Bahir Dar, Ethiopia.)
Tesfaye Kebede
3
(Department of Mathematics, Bahir Dar University, Bahir Dar, Ethiopia.)
الکلمات المفتاحية: Markov chain, Analogue year, exponential distribution, gamma distribution, option price, Teff,
ملخص المقالة :
In this study we model the daily rainfall occurrence using Markov Chain Analogue Yearmodel (MCAYM) and the intensity or amount of daily rainfall using three different probability distributions; gamma, exponential and mixed exponential distributions. Combining the occurrence and intensity model we obtain Markov Chain Analogue Year gamma model (MCAYGM), Markov Chain Analogue Year exponential model (MCAYEM) and Markov Chain Analogue Year mixed exponential model (MCAYMEM). The models are assessed using twenty nine-years(1987-2015) of historical records of daily rainfall data taken from three different locations which are obtained from Ethiopian National Meteorology Agency (ENMA). Both maximum likelihood and least square techniques are used in the estimation of model parameter. The results indicate that all the three model are suitable for the simulation of precipitation process. In order to assess their performance we apply both qualitative (graphical demonstration) and quantitative techniques. In the quantitative, the performance of the three models; MCAYEM, MCAYGM and MCAYMEM are measured using mean absolute error(MAE) and have mean absolute error of 0.45mm, 0.57 mm and 0.42mm respectively for kiremet(June to September) rainfall which is the long rainy season in Ethiopia. These accuracy is mainly because of the new component that is Analogue Year (AY) used in the modeling of frequency of daily rainfall included in the Markov chain (MC) process. Based on these model we obtain an option price for Teff crop for different months. The result shows an excellent accuracy with only maximum absolute error of 0.54 currency.
