119 NTU Management Review Vol. 31 No. 1 Apr. 2021 instrument to hedge the risk of rain; and the CME Hurricane Index (CHI) derivatives due to the devastating impact of Hurricane Katrina. Because of the great loss caused by heavy rainfall disasters2 in Asia in the summer of 2018, the research about the precipitation derivatives can help better deal with these situations in the future. Besides, Lin, Chung, and Yeh (2016), who summarize several pricing methods of weather derivatives published in Taiwan, consider it worthwhile to discuss the valuation of weather derivatives. Therefore, we focus on the valuation and risk management of precipitation derivatives in this paper, hoping to provide reference for the future development of weather derivatives in Taiwan. Though the precipitation can be roughly divided into rainfall and snowfall, the modeling of them is similar and we choose rainfall as the underlying index and take CME Rainfall Index Binary Contracts as a valuation example. Usually, the pricing of weather derivatives includes two steps: first, modeling the behavior of underlying weather index and secondly, pricing the derivatives with a variety of methodologies. In this paper, we choose the occurrence model to describe whether it rains or not by using a first-order, two-state Markov chain with four transition probabilities p00, p01, p10, and p11, which is a widely-used model in valuation and actuarial science as in Lin, Hsu, and Chen (2012). We also choose the magnitude model to describe the daily amount of precipitation with mixed exponential distribution having α, β1 and β2 parameters. For all parameters we mentioned above, including four transition probabilities and three parameters of mixed exponential distribution, we use the truncated Fourier series to describe the seasonal characteristics. The coefficients are estimated by maximum likelihood estimation (MLE). Past literature such as Cao, Li, and Wei (2004), Woolhiser and Pegram (1979), Wilks (2011) and Cabrera, Odening, and Ritter (2013) all witness the application of this type of model. Compared with other models, like the binomial generalized linear models (GLMs) in Shah (2017), the jump Markov process based on the pulse Poisson process in Carmona 2 On August 27, the hourly cumulative precipitation in Setagaya, Tokyo reached 110 mm, causing the subway being forced to stop. The heavy precipitation in Chungcheong-do, South Korea in August was observed at 159 mm, causing many roads and houses to flood. The torrential rainfall disaster on August 23made cities of southern Taiwan drown in water for days. The Kaohsiung Water Resource Bureau reports an estimation of NT$5.56 billion cost for flood control and rainwater drainage planning.
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