Estimating the Value of the Wincat Coupons of the Winterthur Insurance

The three annual 21/4% 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 more than 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 a model, which admits a trend in the expected number of events per observation period, leads to substantially higher knock-out probabilities of the coupons. The estimated discounted value of the coupons drops to Chf 214.44; a conservative evaluation as above leads to substantially lower values. Hence, the model uncertainty is in this case substantially higher than the standard deviations of the used estimators.