Skip to main content Accessibility help
×
Home
Hostname: page-component-99c86f546-md8df Total loading time: 0.347 Render date: 2021-12-01T13:06:27.478Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

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*
Affiliation:
Mathematical Finance, Department of Mathematics, ETH Zürich
*
Mathematical Finance, Department of Mathematics, ETH Zürich, CH-8092 Zürich, Switzerlandschmock@math.ethz.ch
Rights & Permissions[Opens in a new window]

Abstract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Workshop
Copyright
Copyright © International Actuarial Association 1999

Footnotes

1

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

References

[1]Barbour, A.D., Holst, L., and Janson, S., Poisson Approximation, Oxford University Press, Oxford, 1992.Google Scholar
[2]Barndorff-Nielsen, , Information and Exponential Families in Statistical Theory, John Wiley & Sons, Chichester, 1978.Google Scholar
[3]Crédit Suisse First Boston, Fixed Income Research, Convertible bond Winterthur Insurance with Wincat coupons “Hail”, Zürich, January 1997.Google Scholar
[4]Crouhy, M., Galai, D., and Mark, R., Model risk, J. of Financial Engineering 7, no. 3/4 (1998)267288.Google Scholar
[5]Efron, B., and Tibshirani, R.J., An Introduction to the Bootstrap, Chapman & Hall, New York, 1993.CrossRefGoogle Scholar
[6]Embrechts, P., Klüppelberg, C., and Mikosch, T., Modelling Extremal Events for Insurance and Finance, Springer-Verlag, Berlin, 1997.CrossRefGoogle Scholar
[7]Giesbrecht, F., and Kempthorne, O., Maximum likelihood estimation in the three- parameter lognormal distribution, J. Roy. Statist. Soc. Ser. B 38 (1976) 257264.Google Scholar
[8]Hosking, J.R.M., and Wallis, J.R., Parameter and quantile estimation for the generalized Pareto distribution, Technometries 29 (1987) 339349.CrossRefGoogle Scholar
[9]Hinkley, D.V., Inference about the change-point in a sequence of random variables, Biometrika 57 (1970) 117.CrossRefGoogle Scholar
[10]Lehmann, E.L., Testing Statistical Hypotheses, 2. ed., John Wiley & Sons, New York, 1986.CrossRefGoogle Scholar
[11]Linhart, H., and Zucchini, W., Model Selection, John Wiley & Sons, New York, 1986.Google Scholar
[12]McCullagh, P., and Nelder, J.P., Generalized Linear Models, 2. ed., Chapman & Hall, London, 1989.CrossRefGoogle Scholar
[13]Rootzén, H., and Tajvidi, N., Extreme value statistics and wind storm losses: A case study, Scand. Actuarial J. (1997) 7094.Google Scholar
[14]Schiesser, H.-H., et al., Klimatologie der Stürme und Sturmsysteme anhand von Radarund Schadendaten, Vdf, Hochschulverlag AG an der ETH, Zürich, 1997.Google Scholar
[15]Seber, G.A.F., and Wild, C.J., Nonlinear Regression, John Wiley & Sons, New York, 1989.CrossRefGoogle Scholar
[16]Smith, R.L., Maximum likelihood estimation in a class of nonregular cases, Biometrika 72 (1985)6790.CrossRefGoogle Scholar
[17]Venter, G.G., Premium calculation implications of reinsurance without arbitrage, ASTIN Bulletin 21, no. 2 (1991) 223230.CrossRefGoogle Scholar
[18] Winterthur Insurance, Nachrangige Wandelanleihe 1997–2000 von Chf 399'500'000 mit 2¼% WinCAT-Coupons “Hagel”, Emissions- und Kotierungsprospekt.Google Scholar
[19] Winterthur Insurance, 2¼% convertible bond with WinCAT coupon “Hail”, Online information at URL http://www.winterthur.com/prod/wincat/index-e.html.Google Scholar
[20] Winterthur Insurance, The Winterthur Share, Online information at URL http://www.winterthur.com/prod/aktien/index-e.html.Google Scholar
[21] Winterthur Insurance, Hagel und Schäden an Fahrzeugen, Ein Kurzbericht über die Bedrohung in der Schweiz, internal report, January 1997.Google Scholar
[22]Worsley, K.J., Confidence regions and tests for a change-point in a sequence of exponential family random variables, Biometrika 73 (1986) 91104.CrossRefGoogle Scholar
You have Access
28
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

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

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

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

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

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

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *