Comparison of Stochastic and Spline Models for Temperature-based Derivatives in China

In this paper, we propose modelling the seasonal variation of temperature with a stochastic process to achieve normality of residuals. We conduct a heuristic comparison of the new stochastic seasonal variation model with three established empirical temperature and pricing models: the model of Alaton et al., the continuous autoregressive model and the spline model. The test criteria are residual normality, the Akaike information criterion, relative errors, and stability of price behaviour. The objective of the paper is to find the most suitable model for the application of temperature-based derivatives in China. Therefore, 30 years of daily average temperature data from 12 cities in mainland China are applied. The results show that the stochastic seasonal variation model dominates the other three models by providing a more precise fitting of the temperature process. Furthermore, the spline model displays inconsistencies when it is applied to Chinese temperature data. This model has the smallest relative errors, but the worst results for normality of residuals.