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Bias-Free Joint Simulation of Multi-Factor Short Rate Models and Discount Factor
This dissertation explores the use of single- and multi-factor Gaussian short rate models for the valuation of interest rate sensitive European options. Specifically, the focus is on deriving the joint distribution of the short rate and the discount factor, so that an exact and unbiased simulation s...
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| Format: | Thesis |
| Language: | English |
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African Institute of Financial Markets and Risk Management
2019
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| _version_ | 1867613343369396224 |
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| access_status_str | Open Access |
| author | Lopes, Marcio Ferrao |
| author2 | McWalter,Tom |
| author_browse | Lopes, Marcio Ferrao McWalter,Tom |
| author_facet | McWalter,Tom Lopes, Marcio Ferrao |
| author_sort | Lopes, Marcio Ferrao |
| collection | Thesis |
| description | This dissertation explores the use of single- and multi-factor Gaussian short rate models for the valuation of interest rate sensitive European options. Specifically, the focus is on deriving the joint distribution of the short rate and the discount factor, so that an exact and unbiased simulation scheme can be derived for risk-neutral valuation. We see that the derivation of the joint distribution remains tractable when working with the class of Gaussian short rate models. The dissertation compares three joint and exact simulation schemes for the short rate and the discount factor in the single-factor case; and two schemes in the multifactor case. We price European floor options and European swaptions using a twofactor Gaussian short rate model and explore the use of variance reduction techniques. We compare the exact and unbiased schemes to other solutions available in the literature: simulating the short rate under the forward measure and approximating the discount factor using quadrature. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/29396 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:34:38.153Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2019 |
| publishDateRange | 2019 |
| publishDateSort | 2019 |
| publisher | African Institute of Financial Markets and Risk Management |
| publisherStr | African Institute of Financial Markets and Risk Management |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/29396 Bias-Free Joint Simulation of Multi-Factor Short Rate Models and Discount Factor Lopes, Marcio Ferrao McWalter,Tom Kienitz, Jorg Mathematical Finance This dissertation explores the use of single- and multi-factor Gaussian short rate models for the valuation of interest rate sensitive European options. Specifically, the focus is on deriving the joint distribution of the short rate and the discount factor, so that an exact and unbiased simulation scheme can be derived for risk-neutral valuation. We see that the derivation of the joint distribution remains tractable when working with the class of Gaussian short rate models. The dissertation compares three joint and exact simulation schemes for the short rate and the discount factor in the single-factor case; and two schemes in the multifactor case. We price European floor options and European swaptions using a twofactor Gaussian short rate model and explore the use of variance reduction techniques. We compare the exact and unbiased schemes to other solutions available in the literature: simulating the short rate under the forward measure and approximating the discount factor using quadrature. 2019-02-06T13:23:21Z 2019-02-06T13:23:21Z 2018 2019-02-06T07:08:59Z Master Thesis Masters MPhil http://hdl.handle.net/11427/29396 eng application/pdf African Institute of Financial Markets and Risk Management Faculty of Commerce University of Cape Town |
| spellingShingle | Mathematical Finance Lopes, Marcio Ferrao Bias-Free Joint Simulation of Multi-Factor Short Rate Models and Discount Factor |
| thesis_degree_str | Master's |
| title | Bias-Free Joint Simulation of Multi-Factor Short Rate Models and Discount Factor |
| title_full | Bias-Free Joint Simulation of Multi-Factor Short Rate Models and Discount Factor |
| title_fullStr | Bias-Free Joint Simulation of Multi-Factor Short Rate Models and Discount Factor |
| title_full_unstemmed | Bias-Free Joint Simulation of Multi-Factor Short Rate Models and Discount Factor |
| title_short | Bias-Free Joint Simulation of Multi-Factor Short Rate Models and Discount Factor |
| title_sort | bias free joint simulation of multi factor short rate models and discount factor |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/29396 |
| work_keys_str_mv | AT lopesmarcioferrao biasfreejointsimulationofmultifactorshortratemodelsanddiscountfactor |