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Analytical Solution of the Characteristic Function in the Trolle-Schwartz Model
In 2009, Trolle and Schwartz (2008) produced an instantaneous forward interest rate model with several stylised facts such as stochastic volatility. They derived pricing formulae in order to price bonds and bond options, which can be altered to price interest rate options such as caplets, caps and s...
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| Format: | Thesis |
| Language: | English |
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African Institute of Financial Markets and Risk Management
2020
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| _version_ | 1867613180360916992 |
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| access_status_str | Open Access |
| author | Van Gysen, Richard John |
| author2 | McWalter, Thomas |
| author_browse | McWalter, Thomas Van Gysen, Richard John |
| author_facet | McWalter, Thomas Van Gysen, Richard John |
| author_sort | Van Gysen, Richard John |
| collection | Thesis |
| description | In 2009, Trolle and Schwartz (2008) produced an instantaneous forward interest rate model with several stylised facts such as stochastic volatility. They derived pricing formulae in order to price bonds and bond options, which can be altered to price interest rate options such as caplets, caps and swaptions. These formulae involve implementing numerical methods for solving an ordinary differential equation (ODE). Schumann (2016) confirmed the accuracy of the pricing formulae in the Trolle and Schwartz (2008) model using Monte-Carlo simulation. Both authors used a numerical ODE solver to estimate the ODE. In this dissertation, a closed-form solution for this ODE is presented. Two solutions were found. However, these solutions rely on a simplification of the instantaneous volatility function originally proposed in the Trolle and Schwartz (2008) model. This case happens to be the stochastic volatility version of the Hull and White (1990) model. The two solutions are compared to an ODE solver for one stochastic volatility term and then extended to three stochastic volatility terms. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/31328 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:00.945Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2020 |
| publishDateRange | 2020 |
| publishDateSort | 2020 |
| 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:11427/31328 Analytical Solution of the Characteristic Function in the Trolle-Schwartz Model Van Gysen, Richard John McWalter, Thomas Kienitz, Joerg Mathematical Finance In 2009, Trolle and Schwartz (2008) produced an instantaneous forward interest rate model with several stylised facts such as stochastic volatility. They derived pricing formulae in order to price bonds and bond options, which can be altered to price interest rate options such as caplets, caps and swaptions. These formulae involve implementing numerical methods for solving an ordinary differential equation (ODE). Schumann (2016) confirmed the accuracy of the pricing formulae in the Trolle and Schwartz (2008) model using Monte-Carlo simulation. Both authors used a numerical ODE solver to estimate the ODE. In this dissertation, a closed-form solution for this ODE is presented. Two solutions were found. However, these solutions rely on a simplification of the instantaneous volatility function originally proposed in the Trolle and Schwartz (2008) model. This case happens to be the stochastic volatility version of the Hull and White (1990) model. The two solutions are compared to an ODE solver for one stochastic volatility term and then extended to three stochastic volatility terms. 2020-02-25T12:00:49Z 2020-02-25T12:00:49Z 2019 2020-02-25T08:34:58Z Master Thesis Masters MPhil http://hdl.handle.net/11427/31328 eng application/pdf African Institute of Financial Markets and Risk Management Faculty of Commerce |
| spellingShingle | Mathematical Finance Van Gysen, Richard John Analytical Solution of the Characteristic Function in the Trolle-Schwartz Model |
| thesis_degree_str | Master's |
| title | Analytical Solution of the Characteristic Function in the Trolle-Schwartz Model |
| title_full | Analytical Solution of the Characteristic Function in the Trolle-Schwartz Model |
| title_fullStr | Analytical Solution of the Characteristic Function in the Trolle-Schwartz Model |
| title_full_unstemmed | Analytical Solution of the Characteristic Function in the Trolle-Schwartz Model |
| title_short | Analytical Solution of the Characteristic Function in the Trolle-Schwartz Model |
| title_sort | analytical solution of the characteristic function in the trolle schwartz model |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/31328 |
| work_keys_str_mv | AT vangysenrichardjohn analyticalsolutionofthecharacteristicfunctioninthetrolleschwartzmodel |