413
Views
21
CrossRef citations to date
0
Altmetric
SECTION B

Adaptive finite differences and IMEX time-stepping to price options under Bates model

, &
Pages 2515-2529 | Received 02 Feb 2015, Accepted 08 Jun 2015, Published online: 21 Sep 2015
 

Abstract

In this paper, we consider numerical pricing of European and American options under the Bates model, a model which gives rise to a partial-integro differential equation. This equation is discretized in space using adaptive finite differences while an IMEX scheme is employed in time. The sparse linear systems of equations in each time-step are solved using an LU-decomposition and an operator splitting technique is employed for the linear complementarity problems arising for American options. The integral part of the equation is treated explicitly in time which means that we have to perform matrix-vector multiplications each time-step with a matrix with dense blocks. These multiplications are accomplished through fast Fourier transforms. The great performance of the method is demonstrated through numerical experiments.

2010 AMS Subject Classifications:

Acknowledgments

The work in this paper builds on the sequence of Master theses/project reports [Citation31,Citation32,Citation37,Citation38]. The authors are thankful for the early contributions of these students. The computations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) through Uppsala Multidisciplinary Center for Advanced Computational Science (UPPMAX) under Projects snic2014-3-24 and snic2015-6-77. We thank the referees for their suggestions and comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author was financed by the Swedish Research Council under contract number 621-2007-6388.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.