Valuing Asian options using the finite element method and duality techniques

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:222

Article

Foufas, Georgios¹  Larson, Mats G.² 

[1] Chalmers Univ Technol, Dept Math, S-41296 Gothenburg, Sweden

[2] Umea Univ, Dept Math, S-90187 Umea, Sweden

关键词: Finite element method;    Galerkin;    Duality;    A posteriori error estimation;    Mesh refinement;    Adaptivity;    Option pricing;    Brownian motion;    Asian option;    Average option;   

DOI  :  10.1016/j.cam.2007.10.031

来源: Elsevier

【 摘 要 】

The main objective of this paper is to develop an adaptive finite element method for computation of the values, and different sensitivity measures, of the Asian option with both fixed and floating strike. The pricing is based on Black-Scholes PDE-model and a method developed by Vecer where the resulting PDEs are of parabolic type in one spatial dimension and can be applied to both continuous and discrete Asian options. We propose using an adaptive finite element method which is based on a posteriori estimates of the error in desired quantities, which we derive using duality techniques. The a posteriori error estimates are tested and verified, and are used to calculate optimal meshes for each type of option. The use of adapted meshes gives superior accuracy and performance with less degrees of freedom than using uniform meshes. The suggested adaptive finite element method is stable, gives fast and accurate results, and can be applied to other types of options as well. (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free