Volume 7, Issue 2 (Vol.7, No. 2, 2021)
mmr 2021, 7(2): 353-370 |
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Ghasemifard A, Jahandideh M T. Weak Multilevel Path Simulation for Jump-Diffusion Assets. mmr 2021; 7 (2) :353-370
URL: http://mmr.khu.ac.ir/article-1-2778-en.html
URL: http://mmr.khu.ac.ir/article-1-2778-en.html
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
2- Faculty of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran
Abstract: (1753 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 space
for
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
for 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
Type of Study: Original Manuscript |
Subject:
alg
Received: 2018/05/18 | Revised: 2021/08/8 | Accepted: 2020/07/15 | Published: 2021/09/1 | ePublished: 2021/09/1
Received: 2018/05/18 | Revised: 2021/08/8 | Accepted: 2020/07/15 | Published: 2021/09/1 | ePublished: 2021/09/1
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