Weak Multilevel Path Simulation for Jump-Diffusion Assets
This paper, inspired by recent advances in the application of the multilevel Monte-Carlo (MLMC) approach to Lévy driven assets, is based on the valuation of financial derivatives. First, using the weak Euler method the numerical estimate of the underlying asset, which satisfies a multi-dimensional s...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | fas |
| Published: |
Kharazmi University
2021-09-01
|
| Series: | پژوهشهای ریاضی |
| Subjects: | |
| Online Access: | http://mmr.khu.ac.ir/article-1-2778-en.html |
| _version_ | 1797871651634806784 |
|---|---|
| author | Azadeh Ghasemifard Mohammad Taghi Jahandideh |
| author_facet | Azadeh Ghasemifard Mohammad Taghi Jahandideh |
| author_sort | Azadeh Ghasemifard |
| collection | DOAJ |
| description | This paper, inspired by recent advances in the application of the multilevel Monte-Carlo (MLMC) approach to Lévy driven assets, is based on the valuation of financial derivatives. First, using the weak Euler method the numerical estimate of the underlying asset, which satisfies a multi-dimensional stochastic differential equation with Lévy noise, is calculated and then applying the weak multilevel Monte-Carlo method the expected price is obtained. In this paper, as an improvement of Belomestny’s work and with a new approach in the theory, we express and prove the convergence theorems in spacefor and not only 2. We also seek to implement the weak MLMC algorithm for nonlinear equations with dependent components and . In the end, we show numerical experiments when applied to different types of processes with call options../files/site1/files/72/14Abstract.pdf |
| first_indexed | 2024-04-10T00:47:13Z |
| format | Article |
| id | doaj.art-6b2a5db63bca4ef9bcbf7dc95419540c |
| institution | Directory Open Access Journal |
| issn | 2588-2546 2588-2554 |
| language | fas |
| last_indexed | 2024-04-10T00:47:13Z |
| publishDate | 2021-09-01 |
| publisher | Kharazmi University |
| record_format | Article |
| series | پژوهشهای ریاضی |
| spelling | doaj.art-6b2a5db63bca4ef9bcbf7dc95419540c2023-03-13T19:22:49ZfasKharazmi Universityپژوهشهای ریاضی2588-25462588-25542021-09-0172353370Weak Multilevel Path Simulation for Jump-Diffusion AssetsAzadeh Ghasemifard0Mohammad Taghi Jahandideh1 Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran Faculty of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran This paper, inspired by recent advances in the application of the multilevel Monte-Carlo (MLMC) approach to Lévy driven assets, is based on the valuation of financial derivatives. First, using the weak Euler method the numerical estimate of the underlying asset, which satisfies a multi-dimensional stochastic differential equation with Lévy noise, is calculated and then applying the weak multilevel Monte-Carlo method the expected price is obtained. In this paper, as an improvement of Belomestny’s work and with a new approach in the theory, we express and prove the convergence theorems in spacefor and not only 2. We also seek to implement the weak MLMC algorithm for nonlinear equations with dependent components and . In the end, we show numerical experiments when applied to different types of processes with call options../files/site1/files/72/14Abstract.pdfhttp://mmr.khu.ac.ir/article-1-2778-en.htmlnumerical solution of stochastic differential equations (sde)weak multilevel monte-carlo methodweak approximationseuler schemelévy process |
| spellingShingle | Azadeh Ghasemifard Mohammad Taghi Jahandideh Weak Multilevel Path Simulation for Jump-Diffusion Assets پژوهشهای ریاضی numerical solution of stochastic differential equations (sde) weak multilevel monte-carlo method weak approximations euler scheme lévy process |
| title | Weak Multilevel Path Simulation for Jump-Diffusion Assets |
| title_full | Weak Multilevel Path Simulation for Jump-Diffusion Assets |
| title_fullStr | Weak Multilevel Path Simulation for Jump-Diffusion Assets |
| title_full_unstemmed | Weak Multilevel Path Simulation for Jump-Diffusion Assets |
| title_short | Weak Multilevel Path Simulation for Jump-Diffusion Assets |
| title_sort | weak multilevel path simulation for jump diffusion assets |
| topic | numerical solution of stochastic differential equations (sde) weak multilevel monte-carlo method weak approximations euler scheme lévy process |
| url | http://mmr.khu.ac.ir/article-1-2778-en.html |
| work_keys_str_mv | AT azadehghasemifard weakmultilevelpathsimulationforjumpdiffusionassets AT mohammadtaghijahandideh weakmultilevelpathsimulationforjumpdiffusionassets |