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Application of Adjoint Differentiation (AD) for Calculating Libor Market Model Sensitivities
This dissertation explores a key challenge of the financial industry — the efficient computation of sensitivities of financial instruments. The adjoint approach to solving affine recursion problems (ARPs) is presented as a solution to this challenge. A Monte Carlo setting is adopted and it is illust...
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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_ | 1867613143809654784 |
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| access_status_str | Open Access |
| author | Morley, Niall |
| author2 | McWalter, Tom |
| author_browse | McWalter, Tom Morley, Niall |
| author_facet | McWalter, Tom Morley, Niall |
| author_sort | Morley, Niall |
| collection | Thesis |
| description | This dissertation explores a key challenge of the financial industry — the efficient computation of sensitivities of financial instruments. The adjoint approach to solving affine recursion problems (ARPs) is presented as a solution to this challenge. A Monte Carlo setting is adopted and it is illustrated how computational efficiency in sensitivity calculation may be significantly improved via the pathwise derivatives method through adapting an adjoint approach. This is achieved through the reversal of the order of differentiation in the pathwise derivatives algorithm in comparison to the standard, intuitive ‘forward’ approach. The Libor market model (LMM) framework is selected for examples to demonstrate these computational savings, with varying degrees of complexity of the LMM explored, from a one-factor model with constant volatility to a full factor model with time homogeneous volatilities. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/29218 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:28.055Z |
| 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:11427/29218 Application of Adjoint Differentiation (AD) for Calculating Libor Market Model Sensitivities Morley, Niall McWalter, Tom Mathematical Finance This dissertation explores a key challenge of the financial industry — the efficient computation of sensitivities of financial instruments. The adjoint approach to solving affine recursion problems (ARPs) is presented as a solution to this challenge. A Monte Carlo setting is adopted and it is illustrated how computational efficiency in sensitivity calculation may be significantly improved via the pathwise derivatives method through adapting an adjoint approach. This is achieved through the reversal of the order of differentiation in the pathwise derivatives algorithm in comparison to the standard, intuitive ‘forward’ approach. The Libor market model (LMM) framework is selected for examples to demonstrate these computational savings, with varying degrees of complexity of the LMM explored, from a one-factor model with constant volatility to a full factor model with time homogeneous volatilities. 2019-02-04T11:18:06Z 2019-02-04T11:18:06Z 2018 2019-02-04T08:33:29Z Master Thesis Masters MPhil http://hdl.handle.net/11427/29218 eng application/pdf African Institute of Financial Markets and Risk Management Faculty of Commerce University of Cape Town |
| spellingShingle | Mathematical Finance Morley, Niall Application of Adjoint Differentiation (AD) for Calculating Libor Market Model Sensitivities |
| thesis_degree_str | Master's |
| title | Application of Adjoint Differentiation (AD) for Calculating Libor Market Model Sensitivities |
| title_full | Application of Adjoint Differentiation (AD) for Calculating Libor Market Model Sensitivities |
| title_fullStr | Application of Adjoint Differentiation (AD) for Calculating Libor Market Model Sensitivities |
| title_full_unstemmed | Application of Adjoint Differentiation (AD) for Calculating Libor Market Model Sensitivities |
| title_short | Application of Adjoint Differentiation (AD) for Calculating Libor Market Model Sensitivities |
| title_sort | application of adjoint differentiation ad for calculating libor market model sensitivities |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/29218 |
| work_keys_str_mv | AT morleyniall applicationofadjointdifferentiationadforcalculatinglibormarketmodelsensitivities |