A Levy Regime-Switching Temperature Dynamics Model for Weather Derivatives

Abstract

Weather is a key production factor in agricultural crop production but 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 modeling of the underlying weather variable (temperature). In other to circumvent this problem, a novel time-varying mean-reversion L´evy 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 to use the hyperbolic distribution to capture the semi-heavy 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 L´evy 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.