Abstract
Weather is a key production factor in agricultural crop production and at the same time the most significant and least controllable source of peril in agriculture. These effects of weather on agricultural crop production have triggered a widespread support for weather derivatives as a means of mitigating the risk associated with climate change on agriculture. However, these products are faced with basis risk as a result of poor design and modelling of the underlying weather variable (temperature). In order to circumvent these problems, a novel time-varying mean-reversion Lévy regime-switching model is used to model the dynamics of the deseasonalized temperature dynamics. Using plots and test statistics, it is observed that the residuals of the deseasonalized temperature data are not normally distributed. To model the nonnormality in the residuals, we propose using the hyperbolic distribution to capture the semiheavy tails and skewness in the empirical distributions of the residuals for the shifted regime. The proposed regime-switching model has a mean-reverting heteroskedastic process in the base regime and a Lévy process in the shifted regime. By using the Expectation-Maximization algorithm, the parameters of the proposed model are estimated. The proposed model is flexible as it modelled the deseasonalized temperature data accurately.
Highlights
From tilling of the farmland to selling of the output of the crop yield, farmers around the world make countless decisions that affect their performance
We model the residuals εt of the shifted regime by the generalized hyperbolic (GH) distribution and the subclasses which are relevant for applications
The estimated parameters of normal, HYP, GH, normalinverse Gaussian (NIG), and VG distributions are presented in the Table 7
Summary
From tilling of the farmland to selling of the output of the crop yield, farmers around the world make countless decisions that affect their performance. The model of Elias et al (from we will call the model developed by Elias et al as Elias’ Model) failed to capture the fact that volatility of temperature varies with varying temperature as it goes through discrete changes between the states of the regime process. Evarest et al [15] improved on Elias’ model by capturing the fact that volatility of temperature varies as temperature goes through discrete changes between the states of the regime They priced weather derivatives contracts based on the daily temperature dynamics. For the “jump” regime, he used different noise process (Brownian motion with more extreme drift and volatility) to drive the abnormal positive or negative “jumps” in the temperature dynamics He failed to capture the changes in volatility of temperature during the MRS model but rather assumed a constant volatility in both regimes. To the best of our knowledge, the twostate regime-switching model developed is the first kind of model that can be used to price futures and options on futures
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