An efficient numerical method for pricing a Russian option with a finite time horizon

Abstract

In this paper, we present a finite difference scheme for a linear complementarity problem with a mixed boundary condition arising from pricing a Russian option with a finite time horizon. An implicit Euler method for the temporal discretization and second-order difference schemes on a piecewise uniform mesh for the spatial discretization are used to solve the linear complementarity problem with a mixed boundary condition. It is shown that the transformed discrete operator satisfies a maximum principle, which is used to derive the error estimate. It is proved that the scheme is first- and second-order convergent with respect to the temporal and spatial variables, respectively. Numerical experiments verify the validity of the theoretical results.

Keywords:

• Russian option
• option valuation
• linear complementarity problem
• finite difference
• mixed boundary condition

2010 AMS subject classifications:

• 65M06
• 65M12
• 65M15

Acknowledgments

We would like to thank the anonymous reviewers for their valuable suggestions and comments for the improvement of this paper. The work was supported by Major Humanities and Social Sciences Projects in Colleges and Universities of Zhejiang Province (Grant No. 2018GH020).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by Major Humanities and Social Sciences Projects in Colleges and Universities of Zhejiang Province [Grant No. 2018GH020].