Estimating the Value of the Wincat Coupons of the Winterthur Insurance Convertible Bond: A Study of the Model Risk1

The three annual 2¼% 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 6 000 motor vehicles insured with Winterthur Insurance. Data for events, where storm or hail damaged more than 1 000 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.