Modelling temperatures in shanghai using fractional brownian motion

In this study, daily average temperatures in Shanghai over the last twenty years are modelled with a view towards application to weather derivatives. For this purpose, a mean-reverting Ornstein-Uhlenbeck (OU) process driven by Fractional Brownian Motion (FBM) is used. The estimated Hurst parameter shows that temperature dynamics deviate from the assumptions of Brownian motion and that option prices using FBM are significantly higher compared to the model with an OU process driven by Brownian motion. The motivation for using FBM is the long-range temporal dependence and the normality of temperature fluctuations observed for Shanghai temperatures. Standard call and put options on a temperature index (Heating/Cooling Degree Days [HDDs/CDDs]) for Shanghai are priced using a Monte Carlo simulation of the proposed model with fitted parameters.