Parallelizing Computation of Expected Values in Recombinant Binomial Trees
| dc.contributor.author | Popuri, Sai K. | |
| dc.contributor.author | Raim, Andrew M. | |
| dc.contributor.author | Neerchal, Nagaraj K. | |
| dc.contributor.author | Gobbert, Matthias K. | |
| dc.date.accessioned | 2018-09-20T18:59:05Z | |
| dc.date.available | 2018-09-20T18:59:05Z | |
| dc.date.issued | 2017-11-24 | |
| dc.description | This work was written as part of one of the author's official duties as an Employee of the United States Government and is therefore a work of the United States Government. In accordance with 17 U.S.C. 105, no copyright protection is available for such works under U.S. Law. | en_US |
| dc.description.abstract | Recombinant binomial trees are binary trees where each non-leaf node has two child nodes, but adjacent parents share a common child node. Such trees arise in option pricing in finance. For example, an option can be valued by evaluating the expected payoffs with respect to random paths in the tree. The cost to exactly compute expected values over random paths grows exponentially in the depth of the tree, rendering a serial computation of one branch at a time impractical. We propose a parallelization method that transforms the calculation of the expected value into an embarrassingly parallel problem by mapping the branches of the binomial tree to the processes in a multiprocessor computing environment. We also discuss a parallel Monte Carlo method and verify the convergence and the variance reduction behavior by simulation study. Performance results from R and Julia implementations are compared on a distributed computing cluster. | en_US |
| dc.description.sponsorship | The rst author acknowledges nancial support from the UMBC High Performance Computing Facility (HPCF) at the University of Maryland, Baltimore County (UMBC). The hardware used in the computational studies is part of HPCF. The facility is supported by the U.S. National Science Foundation through the MRI program (grant no. CNS{0821258 and CNS{1228778) and the SCREMS program (grant no. DMS{0821311), with additional substantial support from the University of Maryland, Baltimore County (UMBC). See hpcf.umbc.edu for more information on HPCF and the projects using its resources. | en_US |
| dc.description.uri | https://www.tandfonline.com/doi/full/10.1080/00949655.2017.1402898 | en_US |
| dc.format.extent | 18 pages | en_US |
| dc.genre | journal article pre-print | en_US |
| dc.identifier | doi:10.13016/M2ZW18W6J | |
| dc.identifier.citation | Sai K. Popuri, Andrew M. Raim, Nagaraj K. Neerchal & Matthias K. Gobbert (2018) Parallelizing computation of expected values in recombinant binomial trees, Journal of Statistical Computation and Simulation, 88:4, 657-674, DOI: 10.1080/00949655.2017.1402898 | en_US |
| dc.identifier.uri | https://doi.org/10.1080/00949655.2017.1402898 | |
| dc.identifier.uri | http://hdl.handle.net/11603/11338 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Taylor and Francis Online | en_US |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics Department Collection | |
| dc.relation.ispartof | UMBC Faculty Department | |
| dc.rights | This item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please contact the author. | |
| dc.rights | Public Domain Mark 1.0 | * |
| dc.rights.uri | http://creativecommons.org/publicdomain/mark/1.0/ | * |
| dc.subject | Binomial tree | en_US |
| dc.subject | Bernoulli paths | en_US |
| dc.subject | Monte Carlo estimation | en_US |
| dc.subject | option pricing | en_US |
| dc.subject | UMBC High Performance Computing Facility (HPCF) | en_US |
| dc.title | Parallelizing Computation of Expected Values in Recombinant Binomial Trees | en_US |
| dc.type | Text | en_US |