## Estimating the value of the wincat coupons of the Winterthur insurance convertible bond.(English)Zbl 1162.91433

Summary: The three annual $$2\frac 14$$% interest coupons of the Winterthur Insurance convertible bond (face value CHF 4 700) will only be paid out if during their corresponding observation periods no major storm or hail storm on one single day damages at least 6000 motor vehicles insured with Witerthur Insurance. Data for events, where storm or hail damaged more than 1000 insured vehicles, are available for the last ten years. Using a constant-parameter model, the estimated discounted value of the three WINCAT coupons together is CHF 263 29. A conservative evaluation, which accounts for the standard deviation of the estimate, gives a coupon value of CHF 238.25 However, fitting models which admit a trend or a change-point, leads to substantially higher knock-out probabilities of the coupons. The estimated discounted values of the coupons can drop below the above conservative value; a conservative evaluation as above leads to substantially lower values. Hence, already the model uncertainty is higher than the standard deviations of the used estimators. This shows the dominance of the model risk. Consistency, dispersion, robustness and sensitivity of the models are analysed by a simulation study.

### MSC:

 91B30 Risk theory, insurance (MSC2010)
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### References:

 [1] DOI: 10.1093/biomet/57.1.1 · Zbl 0198.51501 [2] DOI: 10.1093/biomet/73.1.91 · Zbl 0589.62016 [3] J. Roy. Statist. Soc. Ser. 38 pp 257– (1976) [4] Modelling Extremal Events for Insurance and Finance (1997) · Zbl 0873.62116 [5] An Introduction to the Bootstrap (1993) [6] J. of Financial Engineering 7 pp 267– (1998) [7] Convertible bond Winterthur Insurance with Wincat coupons ”Hail” (1997) [8] Information and Exponential Families in Statistical Theory (1978) · Zbl 0387.62011 [9] Poisson Approximation (1992) [10] DOI: 10.2143/AST.21.2.2005365 [11] DOI: 10.1093/biomet/72.1.67 · Zbl 0583.62026 [12] Nonlinear Regression (1989) · Zbl 0721.62062 [13] Klimatologie der Stürme und Sturmsysteme anhand von Radarund Schadendaten (1997) [14] Scand. Actuarial J. pp 70– (1997) [15] Generalized Linear Models (1989) [16] Model Selection (1986) · Zbl 0665.62003 [17] Testing Statistical Hypotheses (1986) · Zbl 0608.62020 [18] DOI: 10.1080/00401706.1987.10488243
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