Estimating the Value of the WinCAT Coupons of the Winterthur Insurance Convertible Bond: A Study of the Model Risk

The three annual 2.25% interest coupons of the Winterthur Insurance convertible bond (face value CHF 4700) will only be paid out if during their corresponding observation periods no major storm or hail storm on one single day damages more than 6000 motor vehicles insured with Winterthur 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 valuation, 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. Consistency, dispersion, robustness and sensitivity of the models are analysed by a simulation study.

Keywords: WinCAT coupon, Winterthur Insurance, catastrophe bond, storm, hail, model risk, (generalized) Pareto distribution, generalised extreme value distribution, composite Poisson model, generalized linear model, change-point , peaks over threshold