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Accelerated Adjoint Algorithmic Differentiation with Applications in Finance
Adjoint Differentiation's (AD) ability to calculate Greeks efficiently and to machine precision while scaling in constant time to the number of input variables is attractive for calibration and hedging where frequent calculations are required. Algorithmic adjoint differentiation tools automatically...
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| Format: | Thesis |
| Language: | English |
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Division of Actuarial Science
2017
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| _version_ | 1867613204705705984 |
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| access_status_str | Open Access |
| author | De Beer, Jarred |
| author2 | Ouwehand, Peter |
| author_browse | De Beer, Jarred Ouwehand, Peter |
| author_facet | Ouwehand, Peter De Beer, Jarred |
| author_sort | De Beer, Jarred |
| collection | Thesis |
| description | Adjoint Differentiation's (AD) ability to calculate Greeks efficiently and to machine precision while scaling in constant time to the number of input variables is attractive for calibration and hedging where frequent calculations are required. Algorithmic adjoint differentiation tools automatically generates derivative code and provide interesting challenges in both Computer Science and Mathematics. In this dissertation we focus on a manual implementation with particular emphasis on parallel processing using Graphics Processing Units (GPUs) to accelerate run times. Adjoint differentiation is applied to a Call on Max rainbow option with 3 underlying assets in a Monte Carlo environment. Assets are driven by the Heston stochastic volatility model and implemented using the Milstein discretisation scheme with truncation. The price is calculated along with Deltas and Vegas for each asset, at a total of 6 sensitivities. The application achieves favourable levels of parallelism on all three dimensions implemented by the GPU: Instruction Level Parallelism (ILP), Thread level parallelism (TLP), and Single Instruction Multiple Data (SIMD). We estimate the forward pass of the Milstein discretisation contains an ILP of 3.57 which is between the average range of 2-4. Monte Carlo simulations are embarrassingly parallel and are capable of achieving a high level of concurrency. However, in this context a single kernel running at low occupancy can perform better with a combination of Shared memory, vectorized data structures and a high register count per thread. Run time on the Intel Xeon CPU with 501 760 paths and 360 time steps takes 48.801 seconds. The GT950 Maxwell GPU completed in 0.115 seconds, achieving an 422⇥ speedup and a throughput of 13 million paths per second. The K40 is capable of achieving better performance. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/24888 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:26.116Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2017 |
| publishDateRange | 2017 |
| publishDateSort | 2017 |
| 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:11427/24888 Accelerated Adjoint Algorithmic Differentiation with Applications in Finance De Beer, Jarred Ouwehand, Peter Kuttel, Michelle Mary Mathematical Finance Adjoint Differentiation's (AD) ability to calculate Greeks efficiently and to machine precision while scaling in constant time to the number of input variables is attractive for calibration and hedging where frequent calculations are required. Algorithmic adjoint differentiation tools automatically generates derivative code and provide interesting challenges in both Computer Science and Mathematics. In this dissertation we focus on a manual implementation with particular emphasis on parallel processing using Graphics Processing Units (GPUs) to accelerate run times. Adjoint differentiation is applied to a Call on Max rainbow option with 3 underlying assets in a Monte Carlo environment. Assets are driven by the Heston stochastic volatility model and implemented using the Milstein discretisation scheme with truncation. The price is calculated along with Deltas and Vegas for each asset, at a total of 6 sensitivities. The application achieves favourable levels of parallelism on all three dimensions implemented by the GPU: Instruction Level Parallelism (ILP), Thread level parallelism (TLP), and Single Instruction Multiple Data (SIMD). We estimate the forward pass of the Milstein discretisation contains an ILP of 3.57 which is between the average range of 2-4. Monte Carlo simulations are embarrassingly parallel and are capable of achieving a high level of concurrency. However, in this context a single kernel running at low occupancy can perform better with a combination of Shared memory, vectorized data structures and a high register count per thread. Run time on the Intel Xeon CPU with 501 760 paths and 360 time steps takes 48.801 seconds. The GT950 Maxwell GPU completed in 0.115 seconds, achieving an 422⇥ speedup and a throughput of 13 million paths per second. The K40 is capable of achieving better performance. 2017-08-17T14:14:10Z 2017-08-17T14:14:10Z 2017 Master Thesis Masters MPhil http://hdl.handle.net/11427/24888 eng application/pdf Division of Actuarial Science Faculty of Commerce University of Cape Town |
| spellingShingle | Mathematical Finance De Beer, Jarred Accelerated Adjoint Algorithmic Differentiation with Applications in Finance |
| thesis_degree_str | Master's |
| title | Accelerated Adjoint Algorithmic Differentiation with Applications in Finance |
| title_full | Accelerated Adjoint Algorithmic Differentiation with Applications in Finance |
| title_fullStr | Accelerated Adjoint Algorithmic Differentiation with Applications in Finance |
| title_full_unstemmed | Accelerated Adjoint Algorithmic Differentiation with Applications in Finance |
| title_short | Accelerated Adjoint Algorithmic Differentiation with Applications in Finance |
| title_sort | accelerated adjoint algorithmic differentiation with applications in finance |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/24888 |
| work_keys_str_mv | AT debeerjarred acceleratedadjointalgorithmicdifferentiationwithapplicationsinfinance |