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Pricing index-linked catastrophe bonds via Monte Carlo simulation
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 pro...
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| Format: | Thesis |
| Language: | English |
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Division of Actuarial Science
2016
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| _version_ | 1867613953803157504 |
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| access_status_str | Open Access |
| author | Van der Merwe, Justin |
| author2 | Giuricich, Mario Nicolo |
| author_browse | Giuricich, Mario Nicolo Van der Merwe, Justin |
| author_facet | Giuricich, Mario Nicolo Van der Merwe, Justin |
| author_sort | Van der Merwe, Justin |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/20647 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:44:20.704Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Division of Actuarial Science |
| publisherStr | Division of Actuarial Science |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/20647 Pricing index-linked catastrophe bonds via Monte Carlo simulation Van der Merwe, Justin Giuricich, Mario Nicolo Ouwehand, Peter Mathematical Finance 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. 2016-07-25T07:11:44Z 2016-07-25T07:11:44Z 2016 Master Thesis Masters MPhil http://hdl.handle.net/11427/20647 eng application/pdf Division of Actuarial Science Faculty of Commerce University of Cape Town |
| spellingShingle | Mathematical Finance Van der Merwe, Justin Pricing index-linked catastrophe bonds via Monte Carlo simulation |
| thesis_degree_str | Master's |
| title | Pricing index-linked catastrophe bonds via Monte Carlo simulation |
| title_full | Pricing index-linked catastrophe bonds via Monte Carlo simulation |
| title_fullStr | Pricing index-linked catastrophe bonds via Monte Carlo simulation |
| title_full_unstemmed | Pricing index-linked catastrophe bonds via Monte Carlo simulation |
| title_short | Pricing index-linked catastrophe bonds via Monte Carlo simulation |
| title_sort | pricing index linked catastrophe bonds via monte carlo simulation |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/20647 |
| work_keys_str_mv | AT vandermerwejustin pricingindexlinkedcatastrophebondsviamontecarlosimulation |