@Article{EAJAM-13-4,
author = {Xin, Wen and Song, Haiming and Zhang, Rui and Yutian, Li},
title = {Primal-Dual Active-Set Method for the Valuation of American Exchange Options},
journal = {East Asian Journal on Applied Mathematics},
year = {2023},
volume = {13},
number = {4},
pages = {858--885},
abstract = {<p style="text-align: justify;">An American exchange option is a rainbow option with two underlying assets,
whose pricing model is a two-dimensional free boundary problem and is equivalent to
a parabolic variational inequality problem on a two-dimensional unbounded domain.
The present work proposes an effective numerical method for this complex problem.
We first reduce the problem into a one-dimensional linear complementarity problem
(LCP) on a bounded domain based on a dimension reduction transformation, an a priori
estimate for the optimal exercise boundary, and a far-field truncation technique. This
LCP is then approximated by a finite element method with a geometric partition in the
spatial direction and a backward Euler method with a uniform partition in the temporal
direction. The convergence order of the fully discretized scheme is established as well.
Further, according to the features of the discretized system, a primal-dual active-set
(PDAS) method is imposed to solve this problem to obtain the option price and the
optimal exercise boundary simultaneously. Finally, several numerical simulations are
carried out to verify the theoretical results and effectiveness of the proposed method.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.2022-227.221222},
url = {https://global-sci.com/article/82443/primal-dual-active-set-method-for-the-valuation-of-american-exchange-options}
}