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Functional quantization-based stratified sampling
Functional quantization-based stratified sampling is a method for variance reduction proposed by Corlay and Pagès (2015). This method requires the ability to both create functional quantizers and to sample Brownian paths from the strata defined by the quantizers. We show that product quantizers are...
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| Format: | Thesis |
| Language: | English |
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Division of Actuarial Science
2018
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| _version_ | 1867613337538265088 |
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| access_status_str | Open Access |
| author | Platts, Alexander |
| author2 | McWalter, Thomas |
| author_browse | McWalter, Thomas Platts, Alexander |
| author_facet | McWalter, Thomas Platts, Alexander |
| author_sort | Platts, Alexander |
| collection | Thesis |
| description | Functional quantization-based stratified sampling is a method for variance reduction proposed by Corlay and Pagès (2015). This method requires the ability to both create functional quantizers and to sample Brownian paths from the strata defined by the quantizers. We show that product quantizers are a suitable approximation of an optimal quantizer for the formation of functional quantizers. The notion of functional stratification is then extended to options written on multiple stocks and American options priced using the Longstaff-Schwartz method. To illustrate the gains in performance we focus on geometric brownian motion (GBM), constant elasticity of variance (CEV) and constant elasticity of variance with stochastic volatility (CEV-SV) models. The pricing algorithm is used to price knock-in, knockout, autocall, call on the max and path dependent call on the max options. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/27105 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:34:32.198Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2018 |
| publishDateRange | 2018 |
| publishDateSort | 2018 |
| 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:11427/27105 Functional quantization-based stratified sampling Platts, Alexander McWalter, Thomas Mathematical Finance Functional quantization-based stratified sampling is a method for variance reduction proposed by Corlay and Pagès (2015). This method requires the ability to both create functional quantizers and to sample Brownian paths from the strata defined by the quantizers. We show that product quantizers are a suitable approximation of an optimal quantizer for the formation of functional quantizers. The notion of functional stratification is then extended to options written on multiple stocks and American options priced using the Longstaff-Schwartz method. To illustrate the gains in performance we focus on geometric brownian motion (GBM), constant elasticity of variance (CEV) and constant elasticity of variance with stochastic volatility (CEV-SV) models. The pricing algorithm is used to price knock-in, knockout, autocall, call on the max and path dependent call on the max options. 2018-01-30T10:26:29Z 2018-01-30T10:26:29Z 2017 Master Thesis Masters MPhil http://hdl.handle.net/11427/27105 eng application/pdf Division of Actuarial Science Faculty of Commerce University of Cape Town |
| spellingShingle | Mathematical Finance Platts, Alexander Functional quantization-based stratified sampling |
| thesis_degree_str | Master's |
| title | Functional quantization-based stratified sampling |
| title_full | Functional quantization-based stratified sampling |
| title_fullStr | Functional quantization-based stratified sampling |
| title_full_unstemmed | Functional quantization-based stratified sampling |
| title_short | Functional quantization-based stratified sampling |
| title_sort | functional quantization based stratified sampling |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/27105 |
| work_keys_str_mv | AT plattsalexander functionalquantizationbasedstratifiedsampling |