Accelerated Adjoint Algorithmic Differentiation with Applications in Finance

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dc.contributor.advisorOuwehand, Peteren_ZA
dc.contributor.advisorKuttel, Michelle Maryen_ZA
dc.contributor.authorDe Beer, Jarreden_ZA
dc.date.accessioned2017-08-17T14:14:10Z
dc.date.available2017-08-17T14:14:10Z
dc.date.issued2017en_ZA
dc.description.abstractAdjoint 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.en_ZA
dc.identifier.apacitationDe Beer, J. (2017). <i>Accelerated Adjoint Algorithmic Differentiation with Applications in Finance</i>. (Thesis). University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science. Retrieved from http://hdl.handle.net/11427/24888en_ZA
dc.identifier.chicagocitationDe Beer, Jarred. <i>"Accelerated Adjoint Algorithmic Differentiation with Applications in Finance."</i> Thesis., University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2017. http://hdl.handle.net/11427/24888en_ZA
dc.identifier.citationDe Beer, J. 2017. Accelerated Adjoint Algorithmic Differentiation with Applications in Finance. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - De Beer, Jarred AB - 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. DA - 2017 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2017 T1 - Accelerated Adjoint Algorithmic Differentiation with Applications in Finance TI - Accelerated Adjoint Algorithmic Differentiation with Applications in Finance UR - http://hdl.handle.net/11427/24888 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/24888
dc.identifier.vancouvercitationDe Beer J. Accelerated Adjoint Algorithmic Differentiation with Applications in Finance. [Thesis]. University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2017 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/24888en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDivision of Actuarial Scienceen_ZA
dc.publisher.facultyFaculty of Commerceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematical Financeen_ZA
dc.titleAccelerated Adjoint Algorithmic Differentiation with Applications in Financeen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMPhilen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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