Exponential time integration for fast finite element solutions of some financial engineering problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:224

Article

Rambeerich, N.¹  Tangman, D. Y.¹  Gopaul, A.¹  Bhuruth, M.¹ 

[1] Univ Mauritius, Dept Math, Reduit, Mauritius

关键词: Partial integro-differential equation;    Finite element discretisations;    Exponential time integration;    Jump-diffusion model;   

DOI  :  10.1016/j.cam.2008.05.047

来源: Elsevier

【 摘 要 】

We consider exponential time integration schemes for fast numerical pricing of European, American, barrier and butterfly options when the stock price follows a dynamics described by a jump-diffusion process. The resulting pricing equation which is in the form of a partial integro-differential equation is approximated in space using finite elements. Our methods require the computation of a single matrix exponential and we demonstrate using a wide range of numerical tests that the combination of exponential integrators and finite element discretisations with quadratic basis functions leads to highly accurate algorithms for cases when the jump magnitude is Gaussian. Comparison with other time-stepping methods are,also carried Out to illustrate the effectiveness of our methods. (c) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free