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Pricing of Reinsurance Contracts in the Presence of Catastrophe Bonds

Published online by Cambridge University Press:  09 August 2013

Gareth G. Haslip  and
Vladimir K. Kaishev
Gareth G. Haslip
Affiliation:
Sir John Cass Business School, City University, 106 Bunhill Road, London EC1Y 8TZ, Tel.: +44 (0)789 1691 811, E-Mail: gareth@haslip.co.uk
Vladimir K. Kaishev
Affiliation:
Sir John Cass Business School, City University, 106 Bunhill Road, London EC1Y 8TZ, Tel.: +44 (0)20 7040 8453, E-Mail: v.kaishev@city.ac.uk
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Abstract

A methodology for pricing of reinsurance contracts in the presence of a catastrophe bond is developed. An important advantage of this approach is that it allows for the pricing of reinsurance contracts consistent with the observed market prices of catastrophe bonds on the same underlying risk process.

Within the proposed methodology, an appropriate financial pricing formula is derived, under a market implied risk neutral probability measure for both a catastrophe bond and an aggregate excess of loss reinsurance contract, using a generalised Fourier transform. Efficient numerical methods for the evaluation of this formula, such as the Fast Fourier transform and Fractional Fast Fourier transform, are considered.

The methodology is illustrated on several examples including Pareto and Gamma claim severities.

Keywords

Reinsurancecatastrophe bondsrisk neutral valuationsecuritisationFast Fourier TransformFractional Fast Fourier Transform
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 307 - 329
Copyright
Copyright © International Actuarial Association 2010

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