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

Published online by Cambridge University Press:  29 August 2014

Uwe Schmock
Uwe Schmock*
Affiliation:
Mathematical Finance, Department of Mathematics, ETH Zürich
*
Mathematical Finance, Department of Mathematics, ETH Zürich, CH-8092 Zürich, Switzerlandschmock@math.ethz.ch
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Abstract

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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.

Keywords

Wincat couponWinterthur Insurancecatastrophe bondstormhailmodel risk(generalised) Pareto distributiongeneralised extreme value distributioncomposite Poisson modelgeneralised linear modelchangepointpeaks over threshold
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 29 , Issue 1 , May 1999 , pp. 101 - 163
Copyright
Copyright © International Actuarial Association 1999

Footnotes

1

1991 Mathematics Subject Classification. 62P05 (primary); 90A09 (secondary).

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