scholarly journals A New Spectral Element Method for Pricing European Options Under the Black–Scholes and Merton Jump Diffusion Models

2011 ◽  
Vol 52 (3) ◽  
pp. 499-518 ◽  
Author(s):  
Feng Chen ◽  
Jie Shen ◽  
Haijun Yu
Keyword(s):  
Spectral Element Method ◽  
Jump Diffusion ◽  
Spectral Element ◽  
Diffusion Models ◽  
European Options ◽  
Black Scholes ◽  
Element Method

scholarly journals A combined compact difference scheme for option pricing in the exponential jump-diffusion models

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Rahman Akbari ◽  
Reza Mokhtari ◽  
Mohammad Taghi Jahandideh
Keyword(s):  
Diffusion Model ◽  
Jump Diffusion ◽  
Diffusion Models ◽  
Asset Market ◽  
European Options ◽  
Compact Difference Scheme ◽  
High Order Method ◽  
Compact Difference ◽  
Black Scholes ◽  
Jump Diffusion Model

AbstractIn the present paper, starting with the Black–Scholes equations, whose solutions are the values of European options, we describe the exponential jump-diffusion model of Levy process type. Here, a jump-diffusion model for a single-asset market is considered. Under this assumption the value of a European contingency claim satisfies a general “partial integro-differential equation” (PIDE). With a combined compact difference (CCD) scheme for the spatial discretization, a high-order method is proposed for solving exponential jump-diffusion models. The method is sixth-order accurate in space and second-order accurate in time. A known analytical solution to the model is used to evaluate the performance of the numerical scheme.

scholarly journals The Implementation of Spectral Element Method in a CAE System for the Solution of Elasticity Problems on Hybrid Curvilinear Meshes

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Dmitriy Konovalov ◽  
Anatoly Vershinin ◽  
Konstantin Zingerman ◽  
Vladimir Levin
Keyword(s):  
Mathematical Simulation ◽  
High Performance ◽  
Spectral Element Method ◽  
New Technologies ◽  
Spectral Element ◽  
High Tech ◽  
Engineering Analysis ◽  
Elasticity Problems ◽  
Cae System ◽  
Element Method

Modern high-performance computing systems allow us to explore and implement new technologies and mathematical modeling algorithms into industrial software systems of engineering analysis. For a long time the finite element method (FEM) was considered as the basic approach to mathematical simulation of elasticity theory problems; it provided the problems solution within an engineering error. However, modern high-tech equipment allows us to implement design solutions with a high enough accuracy, which requires more sophisticated approaches within the mathematical simulation of elasticity problems in industrial packages of engineering analysis. One of such approaches is the spectral element method (SEM). The implementation of SEM in a CAE system for the solution of elasticity problems is considered. An important feature of the proposed variant of SEM implementation is a support of hybrid curvilinear meshes. The main advantages of SEM over the FEM are discussed. The shape functions for different classes of spectral elements are written. Some results of computations are given for model problems that have analytical solutions. The results show the better accuracy of SEM in comparison with FEM for the same meshes.

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