137 NTU Management Review Vol. 31 No. 1 Apr. 2021 = + 100 2 + + 100 2 . (4.2) With the parameters estimated in Table 6, we calculate the theoretical expected rainfall index for different θ from 0.5 to -0.5, which is presented in Table 7. 4.4.2 Burn Analysis and Model Performance According to Dorfleitner and Wimmer (2010) and Cabrera et al. (2013), as an actuarial method, burn analysis (BA) is widely used in pricing under physical measure ℙ, which values a derivative by averaging all payoffs that have been realized in the past. Since weather derivatives are considered a substitute for weather insurances, the BA is widely applied as a benchmark approach in practice. We calculate the BA with the historical monthly rainfall index from January 1946 to December 2004. It is noteworthy that the BA cannot be considered equivalent to θ = 0 since BA is under physical measure ℙ and θ = 0 is under the risk-neutral measure ℚθ. The pricing results (θ = 0) are compared with the BA and the real monthly rainfall index of Des Moines, IA, USA in 2005, which are summarized in Table 7. Table 7 Burn Analysis, Real Rainfall Index in 2005 and Theoretical MPR MPR Rainfall Index θ Mar. Apr. May Jun. Jul. Aug. Sept. Oct. 2005 1.6100 4.7300 5.1600 4.6800 3.2800 1.3300 1.4100 0.9200 BA 2.2347 3.2903 4.2604 4.4301 3.7308 3.9024 2.9459 2.3934 (0.6247) (1.4397) (0.8996) (0.2499) (0.4508) (2.5724) (1.5359) (1.4734) -0.50 1.5719 2.2551 2.7541 2.7720 2.6212 2.3586 1.9935 1.8283 -0.40 1.6575 2.4108 3.0005 3.0277 2.8275 2.5529 2.1975 2.0048 -0.30 1.7508 2.5853 3.2863 3.3237 3.0585 2.7725 2.4360 2.2117 -0.20 1.8532 2.7828 3.6237 3.6721 3.3195 3.0235 2.7201 2.4590 -0.10 1.9663 3.0088 4.0304 4.0906 3.6181 3.3142 3.0668 2.7622 0.00 2.0920 3.2710 4.5343 4.6069 3.9645 3.6566 3.5033 3.1460 (0.4820) (1.4590) (0.6257) (0.0731) (0.6845) (2.3266) (2.0933) (2.2260) 0.10 2.2329 3.5804 5.1820 5.2664 4.3734 4.0681 4.0768 3.6547 0.20 2.3923 3.9533 6.0589 6.1516 4.8670 4.5761 4.8791 4.3753 0.30 2.5748 4.4149 7.3444 7.4315 5.4801 5.2255 6.1201 5.5147 0.40 2.7866 5.0076 9.5059 9.5303 6.2715 6.0979 8.4422 7.7498 0.50 3.0365 5.8087 14.4317 14.0177 7.3513 7.3604 15.8938 16.6189
RkJQdWJsaXNoZXIy ODg3MDU=