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
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.
