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:: Volume 7, Issue 2 (Vol.7, No. 2, Summer 2021) ::
mr 2021, 7(2): 353-370 Back to browse issues page
Weak Multilevel Path Simulation for Jump-Diffusion Assets
Azadeh Ghasemifard 1, Mohammad Taghi Jahandideh2
1- Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran , azadeh.ghasemi@math.iut.ac.ir
2- Faculty of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran
Abstract:   (203 Views)
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
Keywords: Numerical solution of stochastic differential equations (SDE), weak Multilevel Monte-Carlo method, Weak approximations, Euler scheme, Lévy process
Full-Text [PDF 832 kb]   (45 Downloads)    
Type of Study: Original Manuscript | Subject: alg
Received: 2018/05/18 | Accepted: 2020/07/15 | Published: 2021/09/1 | ePublished: 2021/09/1
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Ghasemifard A, Jahandideh M T. Weak Multilevel Path Simulation for Jump-Diffusion Assets. mr. 2021; 7 (2) :353-370
URL: http://mmr.khu.ac.ir/article-1-2778-en.html


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Volume 7, Issue 2 (Vol.7, No. 2, Summer 2021) Back to browse issues page
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