131 NTU Management Review Vol. 31 No. 1 Apr. 2021 contracts is quoted in terms of the respective CME rainfall index, in which each point represents $100. Under the Esscher transform measure ℚθ, the expected rainfall index (ERI) at time t is a conditional risk-adjusted expectation adapted to the filtration ℱt ERI(t, τ1, τ2) = E ℚθ ) [I(τ 1, τ2) | ℱt]. (3.11) the risk-neutral pricing formulas of binary call C(t, τ1, τ2) and put P(t, τ1, τ2) are C(t, τ1, τ2) = 100E ℚθ [I(τ 1, τ2) 1{I(τ1 , τ2) > K}| ℱt] - K. (3.12) P(t, τ1, τ2) = K -100E ℚθ [I(τ 1, τ2) 1{I(τ1 , τ2) < K}| ℱt]. (3.13) 4. Empirical Analysis 4.1 Data 4.1.1 Precipitation Derivatives Market Data Table A.1 lists the specifications of the CME Rainfall Index Binary Contracts. We use the daily prices of these contracts (the rainfall binary monthly options), whose market data is obtained from the CME. The contracts are for March 2005 and 2006, which were traded in the OTC market and cleared by CME ClearPort. And the reference station is Des Moines International Airport, U.S. The details are shown in Table A.2 in Appendix A. 4.1.2 Precipitation Data The rainfall data we use is the daily rainfall (in inches) at the Des Moines International Airport, U.S., from January 1, 1946 to December 31, 2004 (59 years in total), provided by the National Oceanic and Atmospheric Administration (NOAA). Table 2 presents the descriptive statistics, in which the kurtosis and skewness of non-zero data show that the daily rainfall is positively skewed and has a fat tail. Table 2 Descriptive Statistics of Historical Daily Rainfall Data Data Count Mean Std Kurtosis Skewness Min Max Zero 15,164 Non-zero 6,386 0.3003 0.4446 16.9431 3.2821 0.01 6.18
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