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

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 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

2010 Mathematics Subject Classification:

Reference: ASTIN Bulletin, Volume 29, No. 1, May 1999, pages 101-163.
"An Addendum and a Short Comment on the Paper" by A. Gisler and P. Frost is on pages 165-171 of the same volume.

The ASTIN Bulletin, started in 1958, is the journal of the ASTIN and AFIR sections of the International Actuarial Association.

DOI: 10.2143/AST.29.1.504608

Charles A. Hachemeister Prize 2000: This paper has won the Charles A. Hachemeister Prize of the American Casualty Actuarial Society. The prize was awarded at the CAS Annual Meeting November 12-15, 2000, in the JW Marriott Hotel in Washington, D.C., about two blocks away from The White House. The Prize is awarded by the CAS for a paper published in the ASTIN Bulletin or presented at an ASTIN/AFIR Colloquium, which is judged to have a significant potential impact on the practice of the North American property/casualty actuaries and is judged to have practicality of application. Secondary criteria include originality, readability and completeness. The CAS is also going to recognize the 'Addendum and a Short Comment on the Paper' written by Alois Gisler and Patrick Frost.

David Garrick Halmstad Memorial Prize 2001: This paper has won the David Garrick Halmstad Memorial Prize. The Board of Directors of the Actuarial Education and Research Fund (AERF) considered it to be the best contribution to actuarial literature published in 1999. The AERF presented this award in conjunction with the annual meeting of the Society of Actuaries held October 21-24, 2001, at the Hilton Riverside Hotel in New Orleans, Louisiana.

The David Garrick Halmstad Prize is given annually for actuarial research in memory of David Halmstad, an Associate of the Society of Actuaries (SOA), for his significant contributions to actuarial science and research. Funds for the prize were contributed in Mr. Halmstad's memory by his friends and colleagues. The fund is administered by the Actuarial Education and Research Fund.

The paper (54 pages including 15 figures, second revised version, April 30, 1999) is available in:

Note: The Postscript file contains 27 different fonts and several figures, printers need enough memory to print the file.

Sponsor: Credit Suisse Group

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