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Dal Moro, Eric. 2022. “The Skewness of Cape-Cod in a Distribution-Free Model.” Variance 15 (2).
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  • Table 1. Reserves, volatility and skewness resulting from the application of the Cape-Cod method
  • Table 2. Mean, standard deviation and skewness of the IBNR distribution resulting from the bootstrapping method
  • Table 3. Mean, standard deviation and skewness of the IBNR distribution resulting from the Mack Chain-Ladder method
  • Table A1. Incremental payments and premiums \(ν_i\)
  • Table A2. Correlation matrix

Abstract

After the chain ladder and the Bornhuetter-Ferguson method, the Cape Cod reserving method is among the most popular methods used to project non-life paid or incurred triangles. For this method, Saluz (2015) developed a stochastic model allowing the estimation of the prediction error resulting from such projections. This stochastic model involves a parameterization of the Cape Cod method based on incremental triangles of incurred or paid. Hence, this parameterized method differs from the usual way in which the Cape Cod is usually applied on cumulative triangles of incurred or paid. Based on this proposed stochastic model, this paper provides a first approach for the estimation of the third moment, i.e., the skewness, of the resulting reserving distribution. In order to apply the proposed estimation method, a numerical example is provided.

Accepted: April 26, 2022 EDT

Appendix A

Table A1.Incremental payments and premiums \(ν_i\)
i / j 0 1 2 3 4 5 6 7 8 9 \(v_{i}\)
0 5,946,975 3,721,237 895,717 207,761 206,704 62,124 65,813 14,850 11,129 15,814 15,473,558
1 6,346,756 3,246,406 723,221 151,797 67,824 36,604 52,752 11,186 11,646 14,882,436
2 6,269,090 2,976,223 847,053 262,768 152,703 65,445 53,545 8,924 14,456,039
3 5,863,015 2,683,224 722,532 190,653 132,975 88,341 43,328 14,054,917
4 5,778,885 2,745,229 653,895 273,395 230,288 105,224 14,525,373
5 6,184,793 2,828,339 572,765 244,899 104,957 15,025,923
6 5,600,184 2,893,207 563,114 225,517 14,832,965
7 5,288,066 2,440,103 528,042 14,550,359
8 5,290,793 2,357,936 14,461,781
9 5,675,568 15,210,363
Table A2.Correlation matrix
i/j 9 8 7 6 5 4 3 2 1
9 100% 76% 63% 40% 30% 22% 16% 10% 5%
8 76% 100% 83% 53% 40% 28% 22% 14% 6%
7 63% 83% 100% 64% 48% 34% 26% 16% 7%
6 40% 53% 64% 100% 75% 54% 40% 26% 11%
5 30% 40% 48% 75% 100% 72% 54% 34% 15%
4 22% 28% 34% 54% 72% 100% 76% 48% 21%
3 16% 22% 26% 40% 54% 76% 100% 64% 28%
2 10% 14% 16% 26% 34% 48% 64% 100% 45%
1 5% 6% 7% 11% 15% 21% 28% 45% 100%