Convergence of Capital and Insurance Markets: Pricing Aspects of Index-Linked Catastrophic Loss Instruments

Gatzert, Nadine; Pokutta, Sebastian; Vogl, Nikolai

doi:10.2139/ssrn.2320370

Cited by 2 publications

(1 citation statement)

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“…We now turn to focusing on a particular type of CocoCat, and introduce the workings, notations and basic definitions necessary for its analytical pricing. We suppose that the trigger is indexlinked, and is furthermore in line with many of the index-linked triggers that CAT bonds are based upon (see, for example, the review by Cummins [19], as well as Haslip and Kaishev [36], Ma and Ma [51], Nowak and Romaniuk [55] and Gatzert et al [30]). As an example, consider one of the most commonly-issued index-linked CAT bonds: the type that is dependent upon the Property Claims Services (PCS) industry index.…”

Section: Model Setup Assumptions and Propertiesmentioning

confidence: 99%

Valuation of contingent convertible catastrophe bonds — The case for equity conversion

Burnecki

Giuricich

Palmowski

2019

Insurance: Mathematics and Economics

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Within the context of the banking-related literature on contingent convertible bonds, we comprehensively formalise the design and features of a relatively new type of insurance-linked security, called a contingent convertible catastrophe bond (CocoCat). We begin with a discussion of its design and compare its relative merits to catastrophe bonds and catastrophe-equity puts. Subsequently, we derive analytical valuation formulae for index-linked CocoCats under the assumption of independence between natural catastrophe and financial markets risks. We model natural catastrophe losses by a time-inhomogeneous compound Poisson process, with the interest-rate process governed by the Longstaff model. By using an exponential change of measure on the loss process, as well as a Girsanov-like transformation to synthetically remove the correlation between the share and interest-rate processes, we obtain these analytical formulae. Using selected parameter values in line with earlier research, we empirically analyse our valuation formulae for index-linked CocoCats. An analysis of the results reveals that the Coco-Cat prices are most sensitive to changing interest-rates, conversion fractions and the threshold levels defining the trigger times.

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Section: Model Setup Assumptions and Propertiesmentioning

confidence: 99%

Valuation of contingent convertible catastrophe bonds — The case for equity conversion

Burnecki

Giuricich

Palmowski

2019

Insurance: Mathematics and Economics

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Pricing of insurance-linked securities: a multi-peril approach

Burnecki,

Teuerle,

Zdeb

2024

J.Math.Industry

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In this paper we build a methodology for pricing of insurance-linked securities which are tied to multiple natural catastrophe perils. As a representative example, we construct a multi-peril catastrophe (CAT) bond which can be linked to the industry loss indices or actual losses incurred by an insurer. We provide pricing formulas for such CAT bonds. We illustrate the introduced methodology on the US natural catastrophe data obtained from Property Claim Services (PCS). Within this dataset, we specifically examine two types of risks: losses associated with wind and thunderstorm events, and those linked to winter storm events. Then, we fit and validate the underlying compound non-homogeneous Poisson processes taking into account the fact that the data are left-truncated. The best fitted loss distributions appear to be Burr and Generalised Extreme Value and for the first peril and log-normal for the second. Finally, we visualise the zero-coupon CAT bond prices for the selected best-fitted models.

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Convergence of Capital and Insurance Markets: Pricing Aspects of Index-Linked Catastrophic Loss Instruments

Cited by 2 publications

References 47 publications

Valuation of contingent convertible catastrophe bonds — The case for equity conversion

Valuation of contingent convertible catastrophe bonds — The case for equity conversion

Pricing of insurance-linked securities: a multi-peril approach

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