Joshi’s Split Tree for Option Pricing
In a thorough study of binomial trees, Joshi introduced the split tree as a two-phase binomial tree designed to minimize oscillations, and demonstrated empirically its outstanding performance when applied to pricing American put options. Here we introduce a “flexible” version of Joshi’s tree, and de...
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MDPI AG
2020-08-01
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| Շարք: | Risks |
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| Առցանց հասանելիություն: | https://www.mdpi.com/2227-9091/8/3/81 |
| _version_ | 1827711880173453312 |
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| author | Guillaume Leduc Merima Nurkanovic Hot |
| author_facet | Guillaume Leduc Merima Nurkanovic Hot |
| author_sort | Guillaume Leduc |
| collection | DOAJ |
| description | In a thorough study of binomial trees, Joshi introduced the split tree as a two-phase binomial tree designed to minimize oscillations, and demonstrated empirically its outstanding performance when applied to pricing American put options. Here we introduce a “flexible” version of Joshi’s tree, and develop the corresponding convergence theory in the European case: we find a closed form formula for the coefficients of <inline-formula><math display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mi>n</mi></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><msup><mi>n</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></semantics></math></inline-formula> in the expansion of the error. Then we define several optimized versions of the tree, and find closed form formulae for the parameters of these optimal variants. In a numerical study, we found that in the American case, an optimized variant of the tree significantly improved the performance of Joshi’s original split tree. |
| first_indexed | 2024-03-10T18:03:45Z |
| format | Article |
| id | doaj.art-fd0c2df4b2ce48289c925b278856ed55 |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-03-10T18:03:45Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
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| spelling | doaj.art-fd0c2df4b2ce48289c925b278856ed552023-11-20T08:44:26ZengMDPI AGRisks2227-90912020-08-01838110.3390/risks8030081Joshi’s Split Tree for Option PricingGuillaume Leduc0Merima Nurkanovic Hot1Department of Mathematics, American University of Sharjah, P.O. Box 26666, Sharjah, UAEDepartment of Mathematics, University of Kaiserslautern, 67653 Kaiserslautern, GermanyIn a thorough study of binomial trees, Joshi introduced the split tree as a two-phase binomial tree designed to minimize oscillations, and demonstrated empirically its outstanding performance when applied to pricing American put options. Here we introduce a “flexible” version of Joshi’s tree, and develop the corresponding convergence theory in the European case: we find a closed form formula for the coefficients of <inline-formula><math display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mi>n</mi></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><msup><mi>n</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></semantics></math></inline-formula> in the expansion of the error. Then we define several optimized versions of the tree, and find closed form formulae for the parameters of these optimal variants. In a numerical study, we found that in the American case, an optimized variant of the tree significantly improved the performance of Joshi’s original split tree.https://www.mdpi.com/2227-9091/8/3/81binomial option pricingerror analysis for non-self-similar binomial treesAmerican optionsBlack–Scholes |
| spellingShingle | Guillaume Leduc Merima Nurkanovic Hot Joshi’s Split Tree for Option Pricing Risks binomial option pricing error analysis for non-self-similar binomial trees American options Black–Scholes |
| title | Joshi’s Split Tree for Option Pricing |
| title_full | Joshi’s Split Tree for Option Pricing |
| title_fullStr | Joshi’s Split Tree for Option Pricing |
| title_full_unstemmed | Joshi’s Split Tree for Option Pricing |
| title_short | Joshi’s Split Tree for Option Pricing |
| title_sort | joshi s split tree for option pricing |
| topic | binomial option pricing error analysis for non-self-similar binomial trees American options Black–Scholes |
| url | https://www.mdpi.com/2227-9091/8/3/81 |
| work_keys_str_mv | AT guillaumeleduc joshissplittreeforoptionpricing AT merimanurkanovichot joshissplittreeforoptionpricing |