Pricing Weather Derivatives Index based on Temperature: The Case of Bahir Dar, Ethiopia

doi:10.5814/j.issn.1674-764X.2019.04.008

Abstract

Abstract:

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.

Key words: continuous-time autoregressive model, seasonality, heating and cooling degree day indices, Bahir Dar

Tesfahun BERHANE,Aemiro SHIBABAW,Gurju AWGICHEW. Pricing Weather Derivatives Index based on Temperature: The Case of Bahir Dar, Ethiopia[J]. Journal of Resources and Ecology, 2019, 10(4): 415-423.

Figures/Tables 14

Fig. 1 Daily average temperature data in Bahir Dar

Fig. 2 Autocorrelation function (ACF) of daily average temperature data in Bahir Dar

Table 1 Estimated value of seasonal parameters

Parameter	a	b	a₁	a₂	b₁	b₂
Value	19.3628	0.0002	1.2086	-0.7071	1.3632	-1.2230

Table 2 Estimates of parameters of AR (3) process

Parameters	${{\beta }_{1}}$	${{\beta }_{2}}$	${{\beta }_{3}}$
Values	$0.56352$	$0.12533$	$0.067029$

Fig. 3 Daily average temperature together with the fitted seasonal function

Fig. 4 The PACF of the residuals of DATs after removing linear trend and seasonal component

Fig. 5 The ACF for the residuals of the AR (3) model of the de-trended and de-seasonalized Bahir Dar average daily data

Fig. 6 The ACF of the squared residuals of the AR (3) model of the de-trended and de-seasonalized Bahir Dar average daily data

Table 3 Estimated value of volatility parameters

Parameters	c	c₁	d₁
Values	0.9686	0.4372	0.0403

Fig. 7 Daily squared volatility together with the fitted volatility function σ2(t)

Fig. 8 The ACF of the squared residuals of the AR (3) model after dividing out the volatility function σ(t) from the regression residuals

Table 4 Estimates of parameters of CAR (3) process volatility parameters

Parameters	${{\alpha }_{1}}$	${{\alpha }_{2}}$	${{\alpha }_{3}}$
Values	$2.43648$	$1.74763$	$0.24086$

Table 5 Observed and simulated values of CDD

Month	Observed	Simulated
April	$99.655$	$102.7946$
May	$102.4135$	$107.4860$
June	$70.005$	$71.2982$

Fig. 9 The monthly evolution of the monthly mean temperature

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