Estimating the Value of the WinCAT Coupons of the Winterthur Insurance Convertible Bond

Uwe Schmock

Abstract: 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 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.

Keywords: WinCAT coupon, Winterthur Insurance, storm, hail, (generalized) Pareto distribution, composite Poisson model, generalized linear model

2010 Mathematics Subject Classification:

Reference: Joint Day Proceedings of the ASTIN/AFIR Colloquia, Cairns 1997, pp. 231-259

DOI: 10.2143/AST.29.1.504608

The paper (29 pages including 12 figures, version June 2, 1997) is available in:

There is also a thoroughly revised and updated version available (55 pages).

Sponsor: Credit Suisse

If you would like to have some comments of Winterthur Insurance, you may send an e-mail to Prof. Dr. Alois Gisler.

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