In this paper we present a stochastic model for daily average temperature to calculate the temperature indices upon which temperature-based derivatives are written. We propose a seasonal mean and volatility model that...In this paper we present a stochastic model for daily average temperature to calculate the temperature indices upon which temperature-based derivatives are written. We propose a seasonal mean and volatility model that describes the daily average temperature behavior using the mean-reverting Ornstein-Uhlenbeck process. We also use higher order continuous-time autoregressive process with lag 3 for modeling the time evolution of the temperatures after removing trend and seasonality. Our model is fitted to 11 years of data recorded, in the period 1 January 2005 to 31 December 2015, Bahir Dar, Ethiopia, obtained from Ethiopia National Meteorological Services Agency. The analytical approximation formulas are used to price heating degree days(HDD) and cooling degree days(CDD) futures. The suggested model is analytically tractable for derivation of explicit prices for CDD and HDD futures and option. The price of the CDD future is calculated, using analytical approximation formulas. Numerical examples are presented to indicate the accuracy of the method. The results show that our model performs better to predict CDD indices.展开更多
Ethiopian coffee price is highly fluctuated and has significant effect on the economy of the country. Conducting a research on forecasting coffee price has theoretical and practical importance.This study aims at forec...Ethiopian coffee price is highly fluctuated and has significant effect on the economy of the country. Conducting a research on forecasting coffee price has theoretical and practical importance.This study aims at forecasting the coffee price in Ethiopia. We used daily closed price data of Ethiopian coffee recorded in the period 25 June 2008 to 5 January 2017 obtained from Ethiopia commodity exchange（ECX） market to analyse coffee prices fluctuation. Here, the nature of coffee price is non-stationary and we apply the Kalman filtering algorithm on a single linear state space model to estimate and forecast an optimal value of coffee price. The performance of the algorithm for estimating and forecasting the coffee price is evaluated by using root mean square error（RMSE）. Based on the linear state space model and the Kalman filtering algorithm, the root mean square error（RMSE） is 0.000016375, which is small enough, and it indicates that the algorithm performs well.展开更多
In this study,we aim at developing a model for option pricing to reduce the risks associated with Ethiopian coffee price fluctuations.We used daily closed Washed Sidama class A Grade3(WSDA3)coffee price recorded in th...In this study,we aim at developing a model for option pricing to reduce the risks associated with Ethiopian coffee price fluctuations.We used daily closed Washed Sidama class A Grade3(WSDA3)coffee price recorded in the period 31 May 2011 to 30 March 2018 obtained from Ethiopia commodity exchange(ECX)market to analyse the price fluctuation.The nature of log-returns of the price is asymmetric(negatively skewed)and exhibits high kurtosis.We used jump diffusion models for modeling and option pricing the coffee price.The method of maximum likelihood is applied to estimate the parameters of the models.We used the root mean square error(RMSE)to test the validation of the models.The values of RMSE for Merton’s and double exponential jump diffusion models are 0.1093 and 0.0783,respectively.These results indicate that the models fit the data very well.We used analytical and Monte Carlo technique to find the call option pricing of WSDA3 price.Based on the empirical results,we concluded that double exponential jump diffusion model is more efficient than Merton’s model for modeling and option pricing of this coffee price.展开更多
This paper aims at the spatiotemporal distribution of rainfall in Ethiopia and developing stochastic daily rainfall model.Particularly,in this study,we used a Markov Chain Analogue Year(MCAY)model that is,Markov Chain...This paper aims at the spatiotemporal distribution of rainfall in Ethiopia and developing stochastic daily rainfall model.Particularly,in this study,we used a Markov Chain Analogue Year(MCAY)model that is,Markov Chain with Analogue year(AY)component is used to model the occurrence process of daily rainfall and the intensity or amount of rainfall on wet days is described using Weibull,Log normal,mixed exponential and Gamma distributions.The MCAY model best describes the occurrence process of daily rainfall,this is due to the AY component included in the MC to model the frequency of daily rainfall.Then,by combining the occurrence process model and amount process model,we developed Markov Chain Analogue Year Weibull model(MCAYWBM),Markov Chain Analogue Year Log normal model(MCAYLNM),Markov Chain Analogue Year mixed exponential model(MCAYMEM)and Markov Chain Analogue Year gamma model(MCAYGM).The performance of the models is assessed by taking daily rainfall data from 21 weather stations(ranging from 1 January 1984–31 December 2018).The data is obtained from Ethiopia National Meteorology Agency(ENMA).The result shows that MCAYWBM,MCAYMEM and MCAYGM performs very well in the simulation of daily rainfall process in Ethiopia and their performances are nearly the same with a slight difference between them compared to MCAYLNM.The mean absolute percentage error(MAPE)in the four models:MCAYGM,MCAYWBM,MAYMEM and MCAYLNM are 2.16%,2.27%,2.25%and 11.41%respectively.Hence,MCAYGM,MCAYWBM,MAYMEM models have shown an excellent performance compared to MCAYLNM.In general,the light tailed distributions:Weibull,gamma and mixed exponential distributions are appropriate probability distributions to model the intensity of daily rainfall in Ethiopia especially,when these distributions are combined with MCAYM.展开更多
文摘In this paper we present a stochastic model for daily average temperature to calculate the temperature indices upon which temperature-based derivatives are written. We propose a seasonal mean and volatility model that describes the daily average temperature behavior using the mean-reverting Ornstein-Uhlenbeck process. We also use higher order continuous-time autoregressive process with lag 3 for modeling the time evolution of the temperatures after removing trend and seasonality. Our model is fitted to 11 years of data recorded, in the period 1 January 2005 to 31 December 2015, Bahir Dar, Ethiopia, obtained from Ethiopia National Meteorological Services Agency. The analytical approximation formulas are used to price heating degree days(HDD) and cooling degree days(CDD) futures. The suggested model is analytically tractable for derivation of explicit prices for CDD and HDD futures and option. The price of the CDD future is calculated, using analytical approximation formulas. Numerical examples are presented to indicate the accuracy of the method. The results show that our model performs better to predict CDD indices.
文摘Ethiopian coffee price is highly fluctuated and has significant effect on the economy of the country. Conducting a research on forecasting coffee price has theoretical and practical importance.This study aims at forecasting the coffee price in Ethiopia. We used daily closed price data of Ethiopian coffee recorded in the period 25 June 2008 to 5 January 2017 obtained from Ethiopia commodity exchange（ECX） market to analyse coffee prices fluctuation. Here, the nature of coffee price is non-stationary and we apply the Kalman filtering algorithm on a single linear state space model to estimate and forecast an optimal value of coffee price. The performance of the algorithm for estimating and forecasting the coffee price is evaluated by using root mean square error（RMSE）. Based on the linear state space model and the Kalman filtering algorithm, the root mean square error（RMSE） is 0.000016375, which is small enough, and it indicates that the algorithm performs well.
文摘In this study,we aim at developing a model for option pricing to reduce the risks associated with Ethiopian coffee price fluctuations.We used daily closed Washed Sidama class A Grade3(WSDA3)coffee price recorded in the period 31 May 2011 to 30 March 2018 obtained from Ethiopia commodity exchange(ECX)market to analyse the price fluctuation.The nature of log-returns of the price is asymmetric(negatively skewed)and exhibits high kurtosis.We used jump diffusion models for modeling and option pricing the coffee price.The method of maximum likelihood is applied to estimate the parameters of the models.We used the root mean square error(RMSE)to test the validation of the models.The values of RMSE for Merton’s and double exponential jump diffusion models are 0.1093 and 0.0783,respectively.These results indicate that the models fit the data very well.We used analytical and Monte Carlo technique to find the call option pricing of WSDA3 price.Based on the empirical results,we concluded that double exponential jump diffusion model is more efficient than Merton’s model for modeling and option pricing of this coffee price.
文摘This paper aims at the spatiotemporal distribution of rainfall in Ethiopia and developing stochastic daily rainfall model.Particularly,in this study,we used a Markov Chain Analogue Year(MCAY)model that is,Markov Chain with Analogue year(AY)component is used to model the occurrence process of daily rainfall and the intensity or amount of rainfall on wet days is described using Weibull,Log normal,mixed exponential and Gamma distributions.The MCAY model best describes the occurrence process of daily rainfall,this is due to the AY component included in the MC to model the frequency of daily rainfall.Then,by combining the occurrence process model and amount process model,we developed Markov Chain Analogue Year Weibull model(MCAYWBM),Markov Chain Analogue Year Log normal model(MCAYLNM),Markov Chain Analogue Year mixed exponential model(MCAYMEM)and Markov Chain Analogue Year gamma model(MCAYGM).The performance of the models is assessed by taking daily rainfall data from 21 weather stations(ranging from 1 January 1984–31 December 2018).The data is obtained from Ethiopia National Meteorology Agency(ENMA).The result shows that MCAYWBM,MCAYMEM and MCAYGM performs very well in the simulation of daily rainfall process in Ethiopia and their performances are nearly the same with a slight difference between them compared to MCAYLNM.The mean absolute percentage error(MAPE)in the four models:MCAYGM,MCAYWBM,MAYMEM and MCAYLNM are 2.16%,2.27%,2.25%and 11.41%respectively.Hence,MCAYGM,MCAYWBM,MAYMEM models have shown an excellent performance compared to MCAYLNM.In general,the light tailed distributions:Weibull,gamma and mixed exponential distributions are appropriate probability distributions to model the intensity of daily rainfall in Ethiopia especially,when these distributions are combined with MCAYM.
