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: (1481 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
![](file:///C:Users1AppDataLocalTempmsohtmlclip11clip_image002.gif)
for
![](file:///C:Users1AppDataLocalTempmsohtmlclip11clip_image004.gif)
and not only 2. We also seek to implement the weak MLMC algorithm for nonlinear equations with dependent components
![](file:///C:Users1AppDataLocalTempmsohtmlclip11clip_image006.gif)
and
![](file:///C:Users1AppDataLocalTempmsohtmlclip11clip_image008.gif)
. In the end, we show numerical experiments when applied to different types of processes with call options.
./files/site1/files/72/14Abstract.pdf
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