the market price of weather risk, nor adjust the model risk of different weather models. Consequently, researches based on modeling and pricing weather derivatives in China can only build their arguments on the models’ performances in terms of modeling underlying weather factors.
Despite that the absence of trading data is restrictive, there still exist plenty of studies aiming to provide precise modeling for weather derivatives in China. To be specific, Goncu [29] applies a seasonal volatility model to capture the fluctuations of the DAT data of Beijing, Shanghai and Shenzhen, thus to price the temperature- based weather derivatives for those three cities. It is claimed that for degree-day options of Beijing and Shanghai, price approximation formulae under the seasonal volatility model tend to produce very close prices with the Monte Carlo simulation. However, HDD option prices of Shenzhen obtained by the two methods tend to diverge in Goncu’s study [29]. Meanwhile, Zong and Ender [7] carry out a model comparison including two temperature models, namely the Alaton model [1] and the CAR model [2], based on the DAT data of twelve Chinese cities. The result indicates that the CAR model provides better fittings to the Chinese DAT data. Further, Sun and Van Kooten [31] apply three different types of models, including Burn Analysis, a stochastic mean-reverting model, and an autoregressive (AR) model, to price derivative contracts written on growth degree-day indices for the Chinese city Etuokeqi. It is argued by Sun and Van Kooten [31] that AR(1) process with a sine function produces the most accurate result in temperature modeling, and the lowest risk premiums of GDD options in Etuokeqi.
Besides studies of modeling temperature-based weather derivatives, Goncu [32] uses a Markov Chain with jumps model for the precipitation time of Chongqing. Additionally, Zhu et al. [33] introduce a drought option, which is written on the temperature-precipitation joint index, for the purpose of hedging agricultural risks caused by droughts. Zhu et al. [33] then price drought options hypothetically using the DAT and the precipitation data of Ji’nan. Furthermore, Lou and Sun [34] suggest to use agricultural insurance contracts written on precipitation and temperature indices to hedge the freezing-damage risk of tea trees. Employing the data of economic losses caused by freezing damage, precipitation and temperature of Zhejiang Province, Lou and Sun [34] estimate the insurance premium rate basing on
Chapter 2. Review of temperature-based weather derivatives
the information diffusion theoretical model, and design the tea tree freezing damage insurance contract with the analytical result.
Chapter 3
A new temperature model with
stochastic volatility
In this chapter, we introduce an innovative type of stochastic temperature models with the attempt to fill in the gap of stochastic volatility modeling of daily average temperature (DAT). The objective is to provide a higher level of goodness-of-fit to the temperature data of Chinese cities, by achieving the normality of model resid- uals. In detail, we propose to model the temperature volatility with an Ornstein- Uhlenbeck (OU) process as an extension of Benth and ¯Saltyn˙e-Benth’s work [24]. Subsquentially, we apply the so-called stochastic seasonal variation (SSV) model to the DAT data of twelve Chinese cities, thus to investigate the model performance. To the best of our knowledge, this model has not been discussed in the literature.
This chapter proceeds as follows. In the next section, we give a brief overview of the DAT data applied in our study of temperature models. In the second sec- tion, we explain the model dynamics of the SSV model with the presentation of its mathematical framework. In the third section, we explain the parameter estima- tion procedure of the SSV model. In the last section, we discuss possible pricing approaches that could be applied based on the SSV model.
3.1
Data overview
In this chapter, we select twelve Chinese cities regarding to the Standard of Climatic Zone Partition of China. It is a typical partition method used by Chinese architects for the purpose of distinguishing construction standards among regions with different climate characteristics. As it is displayed in Figure 3.1, the standard divides the mainland of China into seven climatic zones.
Since the major factors of the partition method are temperature and precipita- tion, we suppose the possibility that it is also valid for our joint modeling of temper- ature derivatives. We are more interested with the four coastal climatic zones I, II, III and IV, as they constitute the eastern part of China which is more economically developed and with a higher chance of issuing weather derivative contracts first. In this study, we select two to three cities from each of these four climatic zones. For
Chapter 3. A new temperature model with stochastic volatility
Figure 3.1: Standard of Climatic Zone Partition of China
the rest of the climatic zones, namely V, VI, and VII, that cover the less developed regions of China, we only include one city per climatic zone. Generally, the climate of the four eastern climatic zones tends to be more humid with a greater amount of precipitation than the three inland climatic zones in the west.
Table 3.1 gives an overview of the DAT samples of the twelve cities considered in this study. Apart from Shanghai, the duration of the data is thirty years from January 1983 to December 2012. Due to the change of meteo-stations, we only obtain twenty years of Shanghai DAT data, which is from January 1993 to December 2012.