Pricing index-linked catastrophe bonds via Monte Carlo simulation

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dc.contributor.advisorGiuricich, Mario Nicoloen_ZA
dc.contributor.advisorOuwehand, Peteren_ZA
dc.contributor.authorVan der Merwe, Justinen_ZA
dc.date.accessioned2016-07-25T07:11:44Z
dc.date.available2016-07-25T07:11:44Z
dc.date.issued2016en_ZA
dc.description.abstractThe pricing framework used in this dissertation allows for the specification of catastrophe risk under the real-world measure. This gives the user a great deal of freedom in the assumptions made about the underlying catastrophe risk process (referred to in this dissertation as the aggregate loss process). Therefore, this dissertation aims to shed light on the effect of various assumptions and considerations on index-linked CAT bond prices based on the Property Claims Services (PCS) index. Also, given the lack of a closed-form solution to the pricing formulae used and the lack of a liquidly-traded secondary market, this dissertation compares two approximation methods to evaluate expressions involving the aggregate loss process: Monte Carlo simulation and a mixed-approximation method. The two price-approximation methods are largely consistent and seem to agree particularly in the upper quantiles of the distribution of the aggregate loss process. Another key consideration is that the third-party estimating the catastrophe losses in North America, PCS, only records catastrophe losses above $25 million. This dissertation therefore also explores the issue of left-truncated data and its effect when estimating the parameters of the aggregate loss process. For this purpose, it introduces a non-parametric approach to compare, in sample, the results of ignoring the threshold and taking it into account. In both these exercises, it becomes apparent that very heavy-tailed distributions need to be used with caution. In the former case, the use of very heavy-tailed distributions places restrictions on the distributions that can be used for the mixed-approximation method. Finally, as a more realistic avenue this dissertation proposes a simple stochastic intensity model to compare with the deterministic intensity model and found that, by parsimony, the deterministic intensity seems to provide a reasonable model for the upper quantiles of the aggregate loss process. The key results of this dissertation are that the pricing of CAT bonds depends on the quantiles of the aggregate loss process, as in evident both when comparing the approximation methods and the deterministic and stochastic intensity functions, and that left-truncation should be taken into account when valuing index-linked CAT bonds using data from PCS.en_ZA
dc.identifier.apacitationVan der Merwe, J. (2016). <i>Pricing index-linked catastrophe bonds via Monte Carlo simulation</i>. (Thesis). University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science. Retrieved from http://hdl.handle.net/11427/20647en_ZA
dc.identifier.chicagocitationVan der Merwe, Justin. <i>"Pricing index-linked catastrophe bonds via Monte Carlo simulation."</i> Thesis., University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2016. http://hdl.handle.net/11427/20647en_ZA
dc.identifier.citationVan der Merwe, J. 2016. Pricing index-linked catastrophe bonds via Monte Carlo simulation. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Van der Merwe, Justin AB - The pricing framework used in this dissertation allows for the specification of catastrophe risk under the real-world measure. This gives the user a great deal of freedom in the assumptions made about the underlying catastrophe risk process (referred to in this dissertation as the aggregate loss process). Therefore, this dissertation aims to shed light on the effect of various assumptions and considerations on index-linked CAT bond prices based on the Property Claims Services (PCS) index. Also, given the lack of a closed-form solution to the pricing formulae used and the lack of a liquidly-traded secondary market, this dissertation compares two approximation methods to evaluate expressions involving the aggregate loss process: Monte Carlo simulation and a mixed-approximation method. The two price-approximation methods are largely consistent and seem to agree particularly in the upper quantiles of the distribution of the aggregate loss process. Another key consideration is that the third-party estimating the catastrophe losses in North America, PCS, only records catastrophe losses above $25 million. This dissertation therefore also explores the issue of left-truncated data and its effect when estimating the parameters of the aggregate loss process. For this purpose, it introduces a non-parametric approach to compare, in sample, the results of ignoring the threshold and taking it into account. In both these exercises, it becomes apparent that very heavy-tailed distributions need to be used with caution. In the former case, the use of very heavy-tailed distributions places restrictions on the distributions that can be used for the mixed-approximation method. Finally, as a more realistic avenue this dissertation proposes a simple stochastic intensity model to compare with the deterministic intensity model and found that, by parsimony, the deterministic intensity seems to provide a reasonable model for the upper quantiles of the aggregate loss process. The key results of this dissertation are that the pricing of CAT bonds depends on the quantiles of the aggregate loss process, as in evident both when comparing the approximation methods and the deterministic and stochastic intensity functions, and that left-truncation should be taken into account when valuing index-linked CAT bonds using data from PCS. DA - 2016 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2016 T1 - Pricing index-linked catastrophe bonds via Monte Carlo simulation TI - Pricing index-linked catastrophe bonds via Monte Carlo simulation UR - http://hdl.handle.net/11427/20647 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/20647
dc.identifier.vancouvercitationVan der Merwe J. Pricing index-linked catastrophe bonds via Monte Carlo simulation. [Thesis]. University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2016 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/20647en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDivision of Actuarial Scienceen_ZA
dc.publisher.facultyFaculty of Commerceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematical Financeen_ZA
dc.titlePricing index-linked catastrophe bonds via Monte Carlo simulationen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMPhilen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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