121 NTU Management Review Vol. 31 No. 1 Apr. 2021 precipitation derivatives literature. First, we extend the methodologies in Cabrera et al. (2013) to price CME rainfall index binary contracts, which have never been valued before. Second, we discuss several observations about the temporal behavior of the MPR θ during the trading period. We especially probe into the risk attitude of the market participants by interpreting the MPR with the definition of the Arrow-Pratt measure of Absolute Risk Aversion (ARA) and sensitivity analysis. Accordingly, we find that the investors could have a more accurate estimation of the rainfall index during the approaching of trading day or when entering the accumulation period. Besides, since many papers like Wu and Chung (2010), Chang, Lin, and Yu (2011), Lo, Lee, and Yu (2013), and Lo, Chang, Lee, and Yu (2020) have focused on the catastrophe risk management, we also find that the influence of local climate conditions and extreme catastrophes plays an important role in the precipitation derivatives market. Last but not least, we find that the investors mainly enter the market for hedging the weather risk, rather than speculating, which may explain the shrinking of this particular derivatives market. In the remaining of this paper, we present the models of precipitation in section 2, and the model of pricing derivatives in section 3. We then discuss the results of empirical analysis in section 4, and draw our conclusions in the last section. 2. The Models of Precipitation Since models for different types of precipitation are similar, we mainly take the daily rainfall model as an example, which is widely applied in Woolhiser and Pegram (1979), Cao et al. (2004), Leobacher and Ngare (2011), and Cabrera et al. (2013). Based on hydrological study, there are four characteristics of daily rainfall: (1) The probability of rainfall occurrence obeys a seasonal pattern; (2) The sequence of rainy and sunny days follows an autoregressive process; (3) The amount of precipitation on a rainy day varies with the seasons; (4) The volatility of the rainfall amount also changes seasonally. Straightforwardly, the first two characteristics describe the occurrence of rainfall, while the other two characteristics describe the magnitude. To model the dynamic process, we build an occurrence model to describe the presence or absence of rainfall, and a magnitude model to feature the amount of rainfall. The daily rainfall index Rt 3 at time t is 3 The daily rainfall index Rt is defined in the CME Rainfall Index Binary Contracts in Table A.1, Appendix A.
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